CN113793003A - Toughness improvement-oriented electric power system maintenance and operation cooperative decision method - Google Patents

Toughness improvement-oriented electric power system maintenance and operation cooperative decision method Download PDF

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CN113793003A
CN113793003A CN202111022289.3A CN202111022289A CN113793003A CN 113793003 A CN113793003 A CN 113793003A CN 202111022289 A CN202111022289 A CN 202111022289A CN 113793003 A CN113793003 A CN 113793003A
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狄方涛
许根利
李忠良
龙洁
李陆
谢黎鹏
董奥冬
王乐
牛君玲
郭琳
史亮
王逸飞
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Jiaozuo Power Supply Co of State Grid Henan Electric Power Co Ltd
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Abstract

The invention relates to a toughness improvement-oriented electric power system maintenance and operation cooperative decision method, which comprises the following steps: step 1), initializing, confirming information such as network parameters, maintenance requirements, weather conditions and the like, and calculating an initial result of combination of a maintenance plan and a unit; step 2), scene generation, namely generating a random scene by using a recursive sampling method according to the equipment forced outage rate model and the covariate state; step 3), updating a loop of the dynamic scene, a, using Lagrange relaxation technology to carry out iterative solution on the cooperative optimization of the overhaul plan and the unit combination under the latest scene, namely an innermost loop; b. because the FOR of the generator is related to the start-stop state of the unit, updating a random scene of the generator by using a recursive sampling method according to the latest collaborative optimization result; performing iterative loop between the steps a and b until the maintenance plan, the unit combination and the dynamic scene are not changed any more; the method has the advantages of comprehensive consideration of covariates and reasonable steps.

Description

Toughness improvement-oriented electric power system maintenance and operation cooperative decision method
Technical Field
The invention relates to the technical field of electric power systems, in particular to a toughness improvement-oriented electric power system maintenance and operation cooperative decision method.
Background
The power system is influenced by internal factors and external factors in operation, such as equipment aging, operation state, weather, environment and the like, the influence factors are collectively referred to as covariates, the covariates introduce more uncertainty to the power system, and the deterioration of the covariates can cause the forced shutdown of the equipment and increase the operation cost of the system, and even cause major power failure accidents; in recent years, major accidents such as power failure in the united states, power failure in india and the like fully explain that when a short-term power system maintenance plan is made, the maintenance plan is combined with a unit to carry out collaborative optimization, and the influence of covariates on the system state is considered.
In the prior art, research is carried out on a maintenance outage plan, a unit combination plan and cooperative optimization of the maintenance outage plan and the unit combination plan of a power system, mixed integer programming, Lagrangian relaxation, Benders decomposition and other optimization methods are introduced into models in the documents, a good calculation effect is obtained, uncertainty of equipment is ignored in most of the existing models, in the documents considering the availability of the equipment in a small amount, the elements are generally assumed to be in the same pressure and health state and have uniform fault distribution, in fact, the assumption is unrealistic, the regional distribution of a large power grid is wide, the aging state, the operation state, the weather environment where the equipment is located and other factors are different, and direct influence of the factors on the maintenance plan and the unit combination is rarely discussed. For the generator, the main influence variables are internal covariates such as an aging state and an operation state, and for the power transmission line, the main influence variables are external covariates such as a weather environment; therefore, it is very necessary to provide a toughness improvement oriented power system overhaul and operation cooperative decision method with comprehensive consideration of covariates and reasonable steps.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a toughness improvement-oriented power system overhauling and running cooperative decision method with comprehensive consideration of covariates and reasonable steps.
The purpose of the invention is realized as follows: a toughness improvement-oriented power system maintenance and operation cooperative decision method comprises the following steps:
step 1), initialization
Confirming information such as network parameters, maintenance requirements, weather conditions and the like, and calculating an initial result of combination of a maintenance plan and a unit;
step 2), scene generation
Generating a random scene by using a recursive sampling method according to the equipment forced outage rate model and the covariate state;
step 3), dynamic scene update cycle
a. In the latest scene, performing iterative solution on the cooperative optimization of the maintenance plan and the unit combination by using a Lagrange relaxation technology, namely, an innermost loop;
firstly, performing collaborative optimization modeling on a maintenance plan and unit combination, wherein the collaborative optimization modeling comprises a target function and corresponding constraint of a problem, and the optimization target of the problem is to minimize the total cost of a system, including the maintenance cost of power generation and transmission equipment, the operation cost of the system and the load loss cost;
(1) the objective function can be expressed as:
Figure BDA0003242309010000021
in the formula, Hi，tAnd Hl，tThe overhaul costs of the generator i and the transmission line l in the hour t are respectively; xi，tAnd Yl，tThe maintenance states of the generator i and the transmission line l in t hours respectively, the offline maintenance is 0 and can be 1, SUi，tAnd SDi，tThe start-up and shut-down costs of the generator i at t hours,
Figure BDA0003242309010000022
and LSm，tIs the unit load shedding cost and load shedding quantity of the mth line in t hours, Fi(Pi，t) The power generation cost of the generator i in t hours, and
Figure BDA0003242309010000031
in the formula ai，biAnd ciIs the cost coefficient, P, of the generator ii，tThe output of the generator i in t hours, the formula can be linearized by a traditional piecewise linearization method or a close approximation method, and it is noted that when the formula is applied to the power market environment, Fi(Pi，t) Represent the competitive bidding price
Fi(Pi，t)＝fi，t·Pi，t
In the formula fi，tIs the bid price of the generator i in t hours.
(2) Maintenance constraints
Figure BDA0003242309010000032
In the formula of MDG，iThe duration of service required for generator i, NT is the total number of hours in the simulation interval, and
Figure BDA0003242309010000033
in the formula
Figure BDA0003242309010000034
And
Figure BDA0003242309010000035
starting time and ending time of the generator i service window respectively, and if the generator service must be complete, i.e. the service must be performed in a continuous period of time until the service is completed
Figure BDA0003242309010000036
gi，t(hi，t) The state variable is the state variable of starting (ending) maintenance of the generator i, the state variable is 1 when the generator i starts (ends) maintenance in t hours, and otherwise the state variable is 0.
(3) System operational constraints
Figure BDA0003242309010000037
In the formula
Figure BDA0003242309010000038
And
Figure BDA0003242309010000039
the lowest output and the highest output of the generator are respectively.
(4) Overhaul operation decision coupling constraints
The generator cannot bear the output during the overhaul period, the transmission line can influence the network topology during the overhaul period,
Figure BDA00032423090100000310
Figure BDA00032423090100000311
b. updating a random scene of the generator by using a recursive sampling method according to the latest collaborative optimization result when the FOR of the generator is related to the start-stop state of the unit;
c. performing iterative loop between the steps a and b, namely intermediate layer loop, until the maintenance plan, the unit combination and the dynamic scene do not change any more;
and 4) solving cost difference coefficients under all the sampled random scenes, judging the overall convergence, returning to the step 2) to generate a new scene if the convergence condition is not met, and entering the next Monte Carlo iteration, namely the outermost layer of circulation until the optimal maintenance plan and unit combination plan under the current sampled random scene are obtained.
In the step 3), because the forced outage rate of the generator is related to the starting and stopping states of the unit, after the optimal maintenance plan and the unit combination scheme are obtained, the forced outage rate of the generator needs to be recalculated, and the random scene of the generator is updated in the whole simulation interval according to a recursive sampling method; on the contrary, the latest random scene can influence the maintenance plan and unit combination scheme again, which is a self-adaptive heuristic process, the dynamic scene is updated according to the optimal plan, the optimal plan is calculated again according to the latest scene until the scene is not updated any more and the optimal maintenance plan and unit combination are not changed any more, so that the optimal solution under the current random scene is obtained.
The innermost circulation in the step 3) is to decompose a main problem to be optimized into a maintenance subproblem and a unit combination subproblem through a Langerian relaxation technology, decouple coupling constraints among the subproblems, update a Lagrange multiplier through a secondary gradient method, and finally obtain the optimal solution of the Monte Carlo process; the parallel optimization algorithm based on Lagrange relaxation comprises the following steps:
when the coupling constraint is loosened, the optimal maintenance plan subproblem and the unit combination subproblem are decoupled, and the decoupled objective function is
Figure BDA0003242309010000041
In the formula ofi，tAnd mui，tFor the lagrange multiplier, the coupling constraint is relaxed in the objective function through the lagrange multiplier, the main problem is decomposed into the following three subproblems which are independent from each other and can be solved in parallel,
generator overhaul sub-problem
Figure BDA0003242309010000051
The subproblem is constrained to be-.
Sub-problem of transmission line maintenance
Figure BDA0003242309010000052
The subproblem is constrained to be-.
Sub problem of unit combination
Figure BDA0003242309010000053
The subproblem is constrained to be-.
The corresponding Lagrangian dual problem is
max f(λ，μ)
Figure BDA0003242309010000054
Updating the multiplier by adopting a secondary gradient method, wherein the updating process is as follows:
If Ii，t＞Xi，t
Figure BDA0003242309010000055
else if Ii，t＜Xi，t
Figure BDA0003242309010000056
else
λi，t＝λi，t
If Jl，t＜Yl，t
Figure BDA0003242309010000061
else if Jl，t＜Yl，t
Figure BDA0003242309010000062
else
μi，t＝μi，t
in the formula (I), the compound is shown in the specification,
Figure BDA0003242309010000063
the iteration step sizes of the rise and the fall respectively,
Figure BDA0003242309010000064
the iteration step size of the rise and the fall respectively.
Modeling the forced outage rate of the equipment in the step 2) through a proportional risk model, wherein the formula is as follows:
Figure BDA0003242309010000065
comprising two parts, a reference function lambda0(t) and a join function Ψ (Z (t)), the reference function describing the basic aging process of the device, and the join functionThe number is used for reflecting the influence of covariates Z (t), random outage of the generator and the transmission line is taken into consideration, and for the generator, Z (t) {0, 1} represents the state of the unit on and off every hour, 0 is shutdown, and 1 is startup; for the power transmission line, z (t) {0, 1, 2} represents the weather state, 0 represents normal weather, 1 represents adverse weather, and 2 represents severe disaster;
the method is used for generating random scenes by a recursive sampling method and mainly comprises the following steps:
firstly, sampling a [0, 1] uniform random variable u as a probability value;
secondly, returning the maximum T to ensure that the fault probability p (T < T) is less than or equal to u.
In step 2, the failure probability p (T < T) is calculated by accumulating in hours, and the calculation process is as follows, assuming that the failure moment is, if given T > T, T is a non-negative integer, then the probability of reliable operation of the equipment in T +1 hour is:
Figure BDA0003242309010000071
the probability of failure at that moment is:
Figure BDA0003242309010000072
the fault probability can be recurred according to hours, the maximum hour T is finally obtained, the maximum hour T meets the condition that P (T is less than T) is less than or equal to u, the equipment has random fault in the next hour, the value of the moment T +1 is returned, namely the sampled equipment random fault moment, during the equipment fault period, the equipment is subjected to fault post-maintenance, and the maintenance time is obtained by index distribution sampling.
Convergence assessment of innermost loop
From the Lagrange relaxation theory, it can be known that the Lagrange relaxation f (λ, μ) of the original problem is the lower bound of the objective function, and when max f (λ, μ) is close enough to the feasible solution of the original problem, the Lagrange optimization process is considered to be converged. Usually, Relative Dual Gap (RDG) is used as the convergence index,
Figure BDA0003242309010000073
in the formula, gamma is a feasible solution of the original problem, phi is the lower boundary of the original problem obtained after Lagrange relaxation, and in the model, gamma corresponds to the value of the target function and phi corresponds to the lower boundary of Lagrange relaxation.
Convergence evaluation of interlayer loops
The outermost layer cycle is a continuously repeated Monte Carlo process, the middle layer cycle is a calculation process in the Monte Carlo process, adaptive iteration is carried out between scene dynamic update and collaborative optimization, the scene does not change when the iteration is ended, and the optimal solution of overhaul and unit combination does not change, namely Xi，t，Yl，t，Ii，t，Jl，tThe middle layer loop converges at this time, as in the last iteration to obtain the optimal solution. Therefore, the following termination conditions are used
Figure BDA0003242309010000081
Where | x | represents the euclidean norm of the matrix,
Figure BDA0003242309010000082
is the optimal solution obtained by the last Lagrange relaxation optimization.
Convergence evaluation of outermost loop
The monte carlo process is based on sampling of random variables, resulting in an uncertainty in the final result. In order to measure the uncertainty of the result and ensure the accuracy of the result, a Coefficient of Variance (CV) is introduced as a final convergence index and satisfies the requirement
Figure BDA0003242309010000083
Where ns is the number of random scenes sampled，CkIs the optimal cost in the kth random scenario,
Figure BDA0003242309010000084
is the average cost under all scenes, and cv is less than or equal to 0.05 which is used as the convergence standard of the Monte Carlo process.
The invention has the beneficial effects that:
1. considering the cooperative optimization, most of the overhaul is arranged in a low-load period, the total cost of system operation is reduced, and the influence on the system caused by overhaul and outage is reduced;
2. the proposed model can quantify the influence of weather, giving the expected cost of system operation;
3. different equipment in the power grid has different aging degrees and different running states, and the weather conditions suffered by the equipment can also be different, so that the running cost of the system can be estimated by mistake and the made maintenance and outage plan is not necessarily reasonable neglecting the influence of the factors;
4. the framework provided by the application is universal and can be used for calculating the influence of other covariates on the total cost of the system, such as equipment maintenance history, common cause faults, human factors and the like;
5. the framework provided by the application can optimize the overhaul time, the forced outage rate of the overhauled equipment is dynamically adjusted, and the overhaul behavior can be optimized through simple expansion, namely, the optimization decision is made on minor overhaul, major overhaul and perfect overhaul (replacement);
6. the proposed model can help operators to evaluate expected cost, consider the influence of covariates and redistribute budget, and also can provide more information for the operators when making maintenance decisions by comparing expected operation cost of systems under different maintenance windows.
Drawings
FIG. 1 is a block diagram of a coordinated decision-making process for overhaul operation according to the present invention.
Fig. 2 is a schematic diagram of a scene dynamic update cycle according to the present invention.
FIG. 3 is a schematic view of the innermost cycle of the invention.
FIG. 4 is a schematic diagram of a 6-bus system and weather effect profile of the present invention.
FIG. 5 is a schematic diagram of the weather conditions and affected circuits of the present invention.
FIG. 6 is a schematic diagram of a 6-bus system service system and load curve in scenario 1 of the present invention.
FIG. 7 is a schematic diagram of a 6-bus system service system and load curve in scenario 2 of the present invention.
FIG. 8 is a schematic diagram of the weather modification and impact circuitry of the 118-bus system of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Example 1
To illustrate the effectiveness of the proposed framework and algorithm, in the examples, example analyses were performed on IEEE 6-bus systems and 118-bus systems. In order to discuss the influence of covariates and collaborative optimization on the system maintenance plan and the unit combination, the following 4 scenarios are used for analyzing the two systems respectively.
Scene 1: the influence of covariates is not considered, and the cooperative optimization of maintenance and unit combination is not considered;
scene 2: considering the influence of covariates and considering the cooperative optimization of overhaul and unit combination;
scene 3: considering the influence of covariates, the dynamic characteristics of weather are added into a model, such as moving paths, intensity change, coverage area, duration and the like, and the cooperative optimization of maintenance unit combination is not considered;
scene 4: on the basis of the scene 3, the cooperative optimization of overhaul and unit combination is considered.
In the example, a maintenance plan is arranged for three generators G1, G2, G3 and a line L7, the maintenance window is 168 hours in the future, the maintenance window may be established in weeks, but the accurate weather state can be obtained only when the maintenance window is close to the window. Fig. 4 shows a 6-bus system and the range of weather effects, adverse weather first occurring at lines L6 and L7 at 72 hours, then moving to the left and turning to bad weather at 82 hours, weather changes and affected lines as shown in fig. 5, assuming that generator service is not staged, line service is allowed to proceed in two stages, and hourly service costs for generators and lines increase at night and on weekends.
Scene 1: considering the influence of covariates and the cooperative optimization of the combination of the overhaul and the plant in the scenario 1, the overhaul plans of the generators G1, G2, G3 and the line L7 are shown in fig. 6, the system first makes the overhaul plan and then makes the plant combination plan, the Load2 is reduced from 60 hours to 65 hours, the expected energy shortage (EENS) of the system is 82.08(MW), the total operating cost of the system under the given operating parameters is 844690 after considering the Load shedding cost of the system, each cost is given in table 1,
TABLE 1 cost and EENS for scenario 1 and scenario 2
Figure BDA0003242309010000101
Figure BDA0003242309010000111
Scene 2: scenario 2 does not consider the effects of covariates, but the overhaul is co-optimized with the crew combination. The maintenance schedules for generators G1, G2, G3 and line L7 are shown in fig. 7. It can be seen that most of the service is scheduled at a lower load stage to reduce system operating costs and improve system reliability. The overhaul and unit combination are optimized in a synergistic mode, and meanwhile, the two aspects are considered, the load shedding of the system does not occur, the overhaul cost is increased, but the total cost is reduced, and the cost is listed in table 1.
Scene 3: scenario 3 takes into account dynamic changes in weather and forced outages of equipment, but does not take into account the co-optimization of the service plan with the crew combination plan. The sampling of the device state is performed according to the proposed recursive sampling method, and generally 20 to 40 random scenes can satisfy the overall convergence condition. In order to ensure the accuracy of the Monte Carlo process, 40 random scenes are sampled in the scene. Scenario 3 does not consider the co-optimization of the service plan and crew combination, so the expected cost is highest in 4 scenarios. If there is no forced outage of the device in the sampled random scene, scene 3 is identical to scene 1. Of the 40 random scenes sampled, 26 did not have a forced outage (same as scene 1), and 14 scenes had a forced outage of the equipment, the final cost variance factor. The EENS in scenario 4 is 402.11MW, the generator G2, the lines L6, L7 are randomly faulted, and G2 and L7 are simultaneously removed from operation in hours 116 and 120, as shown in Table 2. The average cost of scenario 3 is increased by 8.7% compared to scenario 1, which means that if the influence of the equipment running state and weather state is ignored, or random faults of the equipment are ignored, the total running cost of the system is underestimated,
TABLE 2 cost and EENS for different random scenarios in scenario 3
Figure BDA0003242309010000112
Figure BDA0003242309010000121
Scene 4: the scene 4 further analyzes the influence of covariates and cooperative optimization on the maintenance plan and the unit combination, on the basis of the scene 3, the scene 4 performs cooperative optimization on the maintenance plan and the unit combination, 40 random scenes are sampled in total, the final cost variance coefficient is 0.032, the convergence standard is met, under the given parameters, compared with the scene 2, the average cost of the scene 4 is increased by 12%, which reflects the influence of the equipment running state and severe weather, and compared with the scene 3, the cost of the scene 4 is decreased by 20%, which shows that the cooperative optimization method of the maintenance and unit combination can arrange the system to be scheduled and run from the global optimal angle, and reduce the total running cost of the system,
TABLE 3 cost and EENS for different random scenarios in scenario 4
Figure BDA0003242309010000122
118-bus system
In this example, the overhaul window is 672 hours in the future, the overhaul cost per hour is assumed to be unchanged, the overhaul plan and the unit combination of the system are calculated under scenes 1 to 4 respectively, and the dynamic change of the weather is shown in fig. 8;
the four scenario cost calculations and EENS As shown in Table 4, the EENS in the four scenarios is 0 due to the high reliability of the 118-bus system, but the total cost of the system is different from scenario to scenario in order to maintain system reliability. In the scene 1, the cooperative optimization of overhaul and unit combination is not considered, and the total cost is higher than that of the scene 2; the influence of the running state of the unit and weather change on forced shutdown of the equipment is added in the scene 3, and the cost is the highest in the four scenes under the condition of not carrying out maintenance and unit combination cooperative optimization; although scenario 4 co-optimizes the problem on the basis of scenario 3, reducing the expected cost to some extent, the expected cost is still higher than scenario 1 due to the severe weather causing more forced outages.
Expected cost and EENS for four scenarios in Table 4118-bus System
Figure BDA0003242309010000131
All the calculations are realized on a workstation with a main frequency of 2.39-GHz, for a 6-bus system, overhaul optimization needs 5s, unit combination needs 20s, under a given precision, 30-40 iterations are usually required for the cooperative optimization of the two, a dynamic scene updating cycle generally needs 2-3 iterations to converge, and a Monte Carlo process can be satisfied after 20 scenes are sampled, so that for the 6-bus system, the average calculation time of the calculations 1 and 3 is 25s, the average calculation time of the calculations 2 and 4 is about 8h, and the average calculation time of the calculations 2 and 4 in the 118-bus system is about 84 h.
Example 2
A toughness improvement-oriented power system maintenance and operation cooperative decision method comprises the following steps:
step 1), initialization
Confirming information such as network parameters, maintenance requirements, weather conditions and the like, and calculating an initial result of combination of a maintenance plan and a unit;
step 2), scene generation
Generating a random scene by using a recursive sampling method according to the equipment forced outage rate model and the covariate state;
step 3), dynamic scene update cycle
a. In the latest scene, performing iterative solution on the cooperative optimization of the maintenance plan and the unit combination by using a Lagrange relaxation technology, namely, an innermost loop;
and the innermost circulation is to decompose a main problem to be optimized into a maintenance sub-problem and a unit combination sub-problem by a Langerian relaxation technology, decouple the coupling constraints among the sub-problems, update the Lagrange multiplier by a secondary gradient method, and finally obtain the optimal solution of the Monte Carlo process.
b. Because the FOR of the generator is related to the start-stop state of the unit, updating a random scene of the generator by using a recursive sampling method according to the latest collaborative optimization result;
because the forced outage rate of the generator is related to the starting and stopping states of the unit, after the optimal maintenance plan and unit combination scheme is obtained, the forced outage rate of the generator needs to be recalculated, and the random scene of the generator is updated in the whole simulation interval according to a recursive sampling method; on the contrary, the latest random scene can influence the maintenance plan and unit combination scheme again, which is a self-adaptive heuristic process, the dynamic scene is updated according to the optimal plan, the optimal plan is calculated again according to the latest scene until the scene is not updated any more and the optimal maintenance plan and unit combination are not changed any more, so that the optimal solution under the current random scene is obtained.
c. Performing iterative loop between the steps a and b, namely intermediate layer loop, until the maintenance plan, the unit combination and the dynamic scene do not change any more;
and 4) solving cost difference coefficients under all the sampled random scenes, judging the overall convergence, returning to the step 2) to generate a new scene if the convergence condition is not met, and entering the next Monte Carlo iteration, namely the outermost layer of circulation until the optimal maintenance plan and unit combination plan under the current sampled random scene are obtained.

Claims (4)

1. A toughness improvement-oriented electric power system maintenance and operation cooperative decision method is characterized by comprising the following steps: it comprises the following steps:
step 1), initialization
Confirming information such as network parameters, maintenance requirements, weather conditions and the like, and calculating an initial result of combination of a maintenance plan and a unit;
step 2), scene generation
Generating a random scene by using a recursive sampling method according to the equipment forced outage rate model and the covariate state;
step 3), dynamic scene update cycle
a. In the latest scene, performing iterative solution on the cooperative optimization of the maintenance plan and the unit combination by using a Lagrange relaxation technology, namely, an innermost loop;
b. because the FOR of the generator is related to the start-stop state of the unit, updating a random scene of the generator by using a recursive sampling method according to the latest collaborative optimization result;
c. performing iterative loop between the steps a and b, namely intermediate layer loop, until the maintenance plan, the unit combination and the dynamic scene do not change any more;
and 4) solving cost difference coefficients under all the sampled random scenes, judging the overall convergence, returning to the step 2) to generate a new scene if the convergence condition is not met, and entering the next Monte Carlo iteration, namely the outermost layer of circulation until the optimal maintenance plan and unit combination plan under the current sampled random scene are obtained.
2. The toughness-improvement-oriented power system overhaul and operation cooperative decision method as claimed in claim 1, wherein: in the step 3), because the forced outage rate of the generator is related to the start-stop state of the unit, after the optimal maintenance plan and unit combination scheme is obtained, the forced outage rate of the generator needs to be recalculated, and the random scene of the generator is updated in the whole simulation interval according to a recursive sampling method; on the contrary, the latest random scene can influence the maintenance plan and unit combination scheme again, which is a self-adaptive heuristic process, the dynamic scene is updated according to the optimal plan, the optimal plan is calculated again according to the latest scene until the scene is not updated any more and the optimal maintenance plan and unit combination are not changed any more, so that the optimal solution under the current random scene is obtained.
3. The toughness-improvement-oriented power system overhaul and operation cooperative decision method as claimed in claim 1, wherein: the innermost circulation in the step 3) is to decompose a main problem to be optimized into a maintenance subproblem and a unit combination subproblem through a Langerian relaxation technology, decouple coupling constraints among the subproblems, update a Lagrange multiplier through a secondary gradient method, and finally obtain the optimal solution of the Monte Carlo process.
4. The toughness-improvement-oriented power system overhaul and operation cooperative decision method as claimed in claim 1, wherein: the forced outage rate of the equipment in the step 2) is modeled by a proportional risk model, and the formula is as follows:
Figure FDA0003242308000000021
comprising two parts, a reference function lambda0(t) and a connection function Ψ (Z (t)), wherein the reference function is used for describing a basic aging process of the equipment, the connection function is used for reflecting the influence of a covariate Z (t), random outage of the generator and the transmission line is taken into account, and for the generator, Z (t) {0, 1} represents the on-off state of the unit per hour, 0 is off and 1 is on; for the power transmission line, z (t) {0, 1, 2} represents the weather state, 0 represents normal weather, 1 represents adverse weather, and 2 represents severe disaster;
the method is used for generating random scenes by a recursive sampling method and mainly comprises the following steps:
firstly, sampling a [0, 1] uniform random variable u as a probability value;
secondly, returning the maximum T to ensure that the fault probability p (T is less than T) is less than or equal to u;
in step 2, the failure probability p (T < T) is calculated by accumulating in hours, and the calculation process is as follows, assuming that the failure moment is, if given T > T, T is a non-negative integer, then the probability of reliable operation of the equipment in T +1 hour is:
Figure FDA0003242308000000031
the probability of failure at that moment is:
Figure FDA0003242308000000032
the fault probability can be recurred according to hours, the maximum hour T is finally obtained, the maximum hour T meets the condition that P (T is less than T) is less than or equal to u, the equipment has random fault in the next hour, the value of the moment T +1 is returned, namely the sampled equipment random fault moment, during the equipment fault period, the equipment is subjected to fault post-maintenance, and the maintenance time is obtained by index distribution sampling.
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