CN113177717B - Quick evaluation method for toughness of power transmission system based on influence increment sensitivity - Google Patents
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Abstract
The invention discloses a quick evaluation method for toughness of a power transmission system based on influence on incremental sensitivityThe estimation method comprises the following steps: step 1: inputting initial parameters; step 2: enumerating a transmission system N-order fault state set omega N Initializing a fault state counter s to be 1; and step 3: calculating the load loss I of each fault state s s (ii) a And 4, step 4: calculating the incremental influence DeltaI of each fault state s s (ii) a And 5: if s<S, enabling S to be S +1, and returning to the step 3; otherwise, go to step 6; step 6: calculating a toughness evaluation index value R under the typhoon disaster scene 1 1 (ii) a And 7: calculation of R 1 Partial derivatives of the N order, and the like; finally calculating the toughness index R of the power transmission system with the uncertainty of the typhoon; the method can quantitatively calculate the variable quantity of the toughness index of the power transmission system when the fault probability of the power transmission branch changes in different typhoon scenes, and further can quickly calculate the toughness index of the power transmission system considering the uncertainty of the typhoon.
Description
Technical Field
The invention belongs to toughness evaluation of a power transmission system, and particularly relates to a quick toughness evaluation method of the power transmission system based on influence increment sensitivity.
Background
In recent years, the frequency and intensity of extreme natural disaster weather have been on the rise due to global climate change. Typhoon, one of the most serious natural disaster weathers, can cause huge damage to transmission equipment such as transmission lines and transmission towers exposed in the environment in the initial stage of landing, and seriously affects the normal transmission of electric energy. In order to know and master the influence rule of the extreme disasters on the power transmission system, reduce the influence of the extreme disasters on the power transmission system and ensure the safe and reliable operation of the power transmission system, the toughness evaluation of the power transmission system has become a research direction concerned by the academic and industrial fields. Meanwhile, the toughness level of the power transmission system is also considered as one of important scales for planning and designing the power transmission system at the present stage.
At present, many scholars abroad research on toughness evaluation of a power transmission system under typhoon disasters. The loss load frequency index and the expected power shortage amount adopted in the reliability evaluation are also used for evaluating the toughness level of the power transmission system under the typhoon disaster. Documents [1-3] utilize a sequential monte carlo simulation method to calculate a system loss load frequency index (LOLF, times/week) and an expected power shortage index (EENS, MWh/week) to quantify the toughness level of a power transmission system in typhoon disaster weather. Document [4] uses a monte carlo simulation method to calculate a time-varying reliability index and a damage index to reflect the influence of a typhoon disaster on the power supply reliability of a power transmission system and the damage condition of power transmission equipment caused by the typhoon disaster, thereby quantifying the toughness level of the power transmission system in the typhoon disaster. Document [5] quantifies the toughness level of a power transmission system by calculating the average level of load loss of the power transmission system due to the influence of a typhoon disaster by using an influence incremental state enumeration method.
The toughness evaluation indexes and the method can be used for evaluating the toughness level of the power transmission system under the influence of single typhoon disasters. In order to reasonably analyze the toughness level of a power transmission system in the face of extreme typhoon disasters, various typhoon disaster scenes possibly suffered by the area where the power transmission system is located need to be considered, and the influence of different typhoon disaster scenes on the electric energy transmission capacity of the power transmission system is comprehensively analyzed. For each typhoon disaster scene, if the Monte Carlo method is used for sampling the possible fault states, the system topological structures corresponding to the possible fault states are different, so that the power flow equations are different, the power flow equations need to be solved successively to obtain the load loss amount reflecting the power supply capacity of the power transmission system, and further the toughness index of the power transmission system under the influence of the typhoon is obtained. As the number of typhoon scenarios considered increases and the number of fault conditions sampled increases, the total computation time increases substantially. Therefore, it is difficult to perform toughness evaluation index calculation repeatedly for all possible typhoon disaster scenes and fault states caused by the typhoon disaster scenes by using the conventional method under the current calculation conditions. In order to improve the calculation efficiency of the toughness evaluation of the power transmission system on the premise of ensuring the precision, the invention provides a method for quickly evaluating the toughness of the power transmission system based on the influence increment sensitivity.
Reference to the literature
[1]Panteli M,Mancarella P.Modeling and evaluating the resilience of critical electrical power infrastructure to extreme weather events[J].IEEE Systems Journal,2017,11(3):1733-1742.
[2]Panteli M,Mancarella P,Wilkinson S,et al.Assessment of the resilience of transmission networks to extreme wind events[C].2015IEEE Eindhoven PowerTech,Eindhoven,Netherlands,2015.
[3]Espinoza S,Panteli M,Mancarella P,et al.Multi-phase assessment and adaptation of power systems resilience to natural hazards[J].Electric Power Systems Research,2016,136:352-361.
[4]Zhang H,Cheng L,Yao S,et al.Spatial-temporal reliability and damage assessment of transmission networks under hurricanes[J].IEEE Transactions on Smart Grid,2020,11(2):1044-1054.
[5]Liu X,Hou K,Zhao J,et al.A planning-oriented resilience assessment framework for transmission systems under typhoon disasters[J].IEEE Transactions on Smart Grid,2020,11(6):5431-5441.
Disclosure of Invention
The method combines the existing method for enumerating the incremental influence states with the sensitivity analysis method, and provides a method for quickly evaluating the toughness index based on the incremental influence sensitivity, and the method can quantitatively calculate the variable quantity of the toughness index of the power transmission system when the fault probability of the power transmission branch changes in different typhoon scenes through the partial derivative of the toughness evaluation index on the fault probability of the power transmission branch, so that the toughness index of the power transmission system can be quickly calculated. Finally, the advantages of the method in precision and efficiency are verified by using examples.
The invention is implemented by adopting the following technical scheme:
a rapid evaluation method of toughness of a power transmission system based on an influence increment sensitivity, the power transmission system having a toughness evaluation index unit that shifts a loss capacity of a high-order fault state to a loss capacity of a related low-order fault state, characterized in that: the toughness evaluation index unit realizes the quick evaluation of the toughness of the power transmission system by adopting the following steps:
step 1: inputting the highest order N of fault states and typhoon disaster scene set phi in a power transmission system W The number of wind disaster scenes of the main station is W, the occurrence probability of each wind disaster scene and each power transmission branch in each stationInitializing a typhoon disaster scene counter w to be 1 according to the fault probability under the wind disaster scene;
step 2: enumerating a transmission system N-order fault state set omega N The total number S of the fault states in the fault state set is initialized to be 1;
and step 3: calculating the load loss I of each fault state s s ；
And 4, step 4: calculating the influence increment Delta I of each fault state s by using the formula (2-1) s ；
Wherein n is s Number of faulty transmission branches, Ω, of system fault state s sn Is an nth order subset of s; I.C. A s The load loss of the system when the fault state s occurs is represented and can be obtained through calculation of an optimal load reduction model;
and 5: if S < S, let S be S +1, and return to step 3; otherwise, go to step 6;
step 6: calculating toughness evaluation index value R under the typhoon disaster scene 1 by using formula (2-2) and fault probability of each power transmission branch under the typhoon disaster scene 1 ；
And 7: calculating toughness evaluation index value R in typhoon disaster scene 1 Partial derivatives of order N;
and 8: let w be w + 1;
and step 9: calculating toughness evaluation index value R under typhoon disaster scene w according to fault probability of each power transmission branch under typhoon disaster scene w w ；
Step 10: if W is less than W, and go to step 8; otherwise, go to step 11;
step 11: calculating a toughness index R of the power transmission system considering typhoon uncertainty by using a formula (2-3) and the occurrence probability of each typhoon disaster scene;
wherein phi W Representing a set of typhoon disaster scenes; p w Representing the occurrence probability of a certain typhoon disaster scene w; n represents the fault state order of the toughness evaluation index to be considered; omega n Is an n-order fault state set under typhoon disaster w; p is a radical of wm And (3) representing the fault probability of the mth power transmission branch in the fault state s caused by the typhoon disaster scene w.
Further, in the step 9, the index R is evaluated according to the system toughness in the typhoon disaster scene 1 Obtaining the toughness evaluation index R of the power transmission system under the typhoon disaster weather w through a formula (2-4) w Namely:
wherein p is 1 ＝[p 11 ,…,p 1i ,…,p 1M ]Representing a vector formed by fault probabilities of all power transmission branches under typhoon disaster weather obtained by first simulation; Δ p of w ＝[Δp w1 ,…,Δp wi ,…,Δp wM ]And representing a vector consisting of the fault probability of each power transmission branch in the typhoon disaster scene w obtained through simulation and the change value of the fault probability of each power transmission branch in the typhoon disaster weather obtained through first simulation.
Advantageous effects
The method combines an influence increment state enumeration method with a sensitivity aspect, firstly transfers the loss load quantity of a high-order fault state into the loss load quantity of a related low-order fault state by using the influence increment state enumeration method, improves the proportion of the low-order fault state in the toughness evaluation index, reduces the number of fault states to be considered, then quantitatively calculates the toughness evaluation index of the power transmission system when the fault probability of a power transmission branch is changed due to typhoon disasters of different strengths by using a sensitivity method, and further can quickly calculate the toughness evaluation index of the power transmission system considering the uncertainty of the typhoon disasters by using the method under the condition of not additionally performing optimal power flow calculation.
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FIG. 1 is a flow chart of the present invention.
Fig. 2 is a schematic diagram of the IEEE-RTS79 geographical location of the present invention.
Detailed Description
The invention is described in detail below with reference to the accompanying drawing 1:
due to uncertainty of typhoon disaster weather and randomness of operation conditions of power transmission branches, the toughness evaluation of the power transmission system needs to consider fault states of the power transmission system caused by different typhoon disaster scenes. In order to reduce the number of fault states to be considered in the evaluation process, the incremental state enumeration method is influenced and introduced into the calculation of the toughness evaluation index. The basic idea of the method is to transfer the load loss amount of the high-order fault state to the load loss amount of the related low-order fault state, so that the proportion of the low-order fault state in the toughness evaluation index is improved. Therefore, after combining the state enumeration method based on the influence increment and the power transmission system toughness assessment index, the power transmission system toughness assessment index considering the influence of the typhoon uncertainty can be obtained by the formula (3-1):
wherein phi W Representing a set of typhoon disaster scenes; p w Representing the occurrence probability of a certain typhoon disaster scene w; n represents the fault state order of the toughness evaluation index to be considered; omega n Is an n-order fault state set under typhoon disaster w; p is a radical of wm Representing the fault probability of the mth power transmission branch in the fault state s caused by the typhoon disaster scene w; delta I s The incremental influence of the system in the event of a fault state s to be taken into account is shown, which can be determined from equation (3-2):
wherein n is s Number of faulty transmission branches, Ω, of system fault state s sn Is an nth order subset of s; i is s The load loss of the system when the fault state s occurs can be calculated through an optimal load reduction model.
Assuming that fluctuation of load is not considered, the toughness evaluation index in the typhoon disaster scene with different strength is only related to the fault probability of the power transmission branch in each fault state caused by each typhoon disaster scene. Therefore, the toughness evaluation index of the power transmission system can be calculated by combining a sensitivity analysis method and an influence increment state enumeration method. The toughness evaluation index of the power transmission system when the fault probability of the power transmission branch changes due to typhoon disaster weather of different strengths is calculated quantitatively through the partial derivative of the toughness evaluation index under the influence of the typhoon disaster scene on the fault probability of the power transmission branch, and then the toughness evaluation index of the power transmission system can be calculated rapidly under the condition that optimal power flow calculation is not additionally carried out. Therefore, for a power transmission system comprising M power transmission branches, the toughness evaluation index R of the power transmission system is evaluated in a scene 1 with a concentrated typhoon disaster scene 1 Can be obtained by the formula (3-3).
Evaluating an index R according to the system toughness under the typhoon disaster scene 1 1 As a result, the toughness evaluation index R of the power transmission system in the typhoon disaster weather w can be obtained by the formula (3-4) w 。
Wherein p is 1 ＝[p 11 ,…,p 1i ,…,p 1M ]Representing a vector formed by fault probabilities of all power transmission branches under typhoon disaster weather obtained by first simulation; Δ p w ＝[Δp w1 ,…,Δp wi ,…,Δp wM ]Representing each of the simulated typhoon disaster scenes wAnd the transmission branch fault probability and the variation value of each transmission branch fault probability under the typhoon disaster weather obtained by the first simulation form a vector.
In the formula (3-4), R 1 The first partial derivative of the fault probability for transmission branch i is:
wherein, the first and the second end of the pipe are connected with each other,
representing a fault state set related to the power transmission branch i in the n-order fault state set; p is a radical of m And the fault probability of the power transmission branch m under the typhoon disaster weather obtained by the first simulation is shown.
In equation (3-4), R is for n power transmission branches from power transmission branch i to power transmission branch k 1 The partial derivatives of order n (n ≧ 2) for their failure probabilities are:
wherein the content of the first and second substances,
representing a set of fault conditions associated with all of transmission branches i through k in an n-order fault condition; m ≠ i, …, m ≠ k, meaning that power transmission branch m is not any of power transmission branches i through k.
FIG. 1 is a flow chart of the method, which comprises the following steps:
step 1: inputting the highest order N of the fault state and a typhoon disaster scene set phi W The number of main station wind disaster scenes is W, the occurrence probability of each station wind disaster scene, the fault probability of each power transmission branch under each station wind disaster scene, and an initialized station wind disaster scene counter W is 1.
Step 2: enumerating a transmission system N-order fault state set omega N Aggregation of Fault states Total Fault statesThe number S, the initial failure state counter S is 1.
And step 3: calculating the load loss I of each fault state s s 。
And 4, step 4: calculating the influence increment Delta I of each fault state s by using a formula (3-2) s 。
And 5: if S < S, let S be S +1, and return to step 3; otherwise, go to step 6.
Step 6: calculating a toughness evaluation index value R under the typhoon disaster scene 1 by using a formula (3-3) and the fault probability of each power transmission branch under the typhoon disaster scene 1 1 。
And 7: r was calculated by using the formulas (3-5) to (3-6) 1 Partial derivatives of order N.
And 8: let w be w + 1.
And step 9: calculating a toughness evaluation index value R under the typhoon disaster scene w by using a formula (3-4) and the fault probability of each power transmission branch under the typhoon disaster scene w w 。
Step 10: if W is less than W, go to step 8; otherwise, go to step 11.
Step 11: and (3) calculating the toughness index R of the power transmission system considering the typhoon uncertainty by using the formula (3-1) and the occurrence probability of each typhoon disaster scene.
The method was tested on an IEEE-RTS79 system. The system comprises 24 nodes, 32 generator sets and 38 branches, and peak loads are 2850MW respectively. Wherein, 38 branches include that 5 transformer branches, 1 cable branch and 32 transmission branch constitute. Since transformers generally have high structural reliability and cables are generally laid underground, they are not susceptible to typhoon disasters, and therefore, only faults caused by typhoon disasters to power transmission branches are considered herein. The system is arranged in the Guangdong coastal area, and a typhoon disaster scene set and the fault probability of the power transmission branch under each typhoon disaster scene in the Guangdong coastal area can be obtained according to the literature [5 ]. The geographical location of the system is shown in figure 2.
Randomly selecting a certain typhoon disaster w in a typhoon disaster scene set, wherein the initial typhoon air pressure difference delta H under the typhoon disaster w 0 ＝60.75hPa、Typhoon moving direction angle theta-54 DEG and typhoon moving speed v T 29.25m/s and a typhoon landing point (112.3008 ° E,21.7062 ° N). Computing toughness evaluation index R by using influence increment state enumeration method w The calculation result and the calculation time are recorded in table 2 as references. The calculation results of the method for influencing the incremental sensitivity are also recorded in the table 2, and the toughness evaluation index calculation results under the influence of the typhoon mangosteen and the corresponding sensitivity of each order are utilized in the calculation process.
TABLE 1 toughness index calculation results of power transmission system in typhoon scene w
As can be seen from the table 1, the evaluation index result calculated by the method for the incremental sensitivity of influence provided by the invention under the single typhoon disaster scene w is the same as the reference value, but the calculation time is far shorter than the time directly calculated by the reference method. When the toughness index of the planning-oriented power transmission system is calculated, the toughness evaluation index under the influence of different typhoon disasters needs to be calculated for many times, so that the calculation efficiency can be greatly improved on the premise of ensuring that the calculation accuracy is unchanged by using the method.
In order to verify the applicability and rapidity of the method in toughness evaluation calculation considering typhoon uncertainty, the method firstly utilizes an incremental influence state enumeration method to respectively calculate the toughness index R of the power transmission system in each typhoon scene w Then, the toughness index is calculated by using the formula (3-1) and the occurrence probability of each typhoon disaster scene, and the calculation result and the calculation time are used as the reference. The results of calculations using the method of affecting incremental sensitivity proposed by the present invention are shown in table 2. As can be seen from table 2, compared with the method of directly using the incremental influence sensitivity, the method of the present invention greatly increases the calculation efficiency on the premise of maintaining the calculation accuracy unchanged, and has good applicability to the calculation of the toughness index of the power transmission system considering the typhoon uncertainty.
TABLE 2 toughness index calculation results for transmission systems
The computer hardware configuration comprises an Intel Core i5-6500CPU and an 8G memory, an operating system is windows10, simulation software is MATLAB2020a, and load flow operation of an optimal load reduction model is calculated by using a matpower toolkit.
Inputting the highest order N and typhoon disaster scene set phi in fault state W After a series of data such as the number of total station wind disaster scenes being W, the occurrence probability of each station wind disaster scene, the fault probability of each power transmission branch in each station wind disaster scene and the like, a power transmission system N-order fault state set omega is enumerated first N Calculating the load loss amount and the corresponding influence increment of each fault state; secondly, calculating toughness indexes in the 1 st scene in a typhoon disaster scene set by using a formula (3-3), and calculating N-order partial derivatives of the toughness indexes related to the fault probability of each power transmission branch by using formulas (3-5) and (3-6); then, calculating the toughness index of each typhoon disaster scene by using a formula (3-4); and finally, calculating the toughness index of the power transmission system considering typhoon uncertainty by using the occurrence probability and the corresponding toughness index of each typhoon disaster scene and using a formula (3-1).
The present invention is not limited to the above-described embodiments. The foregoing description of the specific embodiments is intended to describe and illustrate the technical solutions of the present invention, and the above specific embodiments are merely illustrative and not restrictive. Those skilled in the art can make many changes and modifications to the invention without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (1)
1. A quick evaluation method for toughness of a power transmission system based on influence increment sensitivity is characterized in that; the method comprises the following steps:
step 1: inputting the highest order N of fault states in a power transmission system and a typhoon disaster scene set phi W The number of main station wind disaster scenes is W, the occurrence probability of each station wind disaster scene and the fault probability of each power transmission branch under each station wind disaster scene, and a counter W of the initialized station wind disaster scenes is 1;
step 2: enumerating a transmission system N-order fault state set omega N The total number S of the fault states in the fault state set is initialized to be 1;
and step 3: calculating the load loss I of each fault state s s ；
And 4, step 4: calculating the influence increment Delta I of each fault state s by using the formula (1-1) s ；
Wherein n is s Number of faulty transmission branches, Ω, of system fault state s sn Is an nth order subset of s; i is s The load loss of the system when the fault state s occurs is represented and can be obtained through calculation of an optimal load reduction model;
and 5: if S < S, let S be S +1, and return to step 3; otherwise, go to step 6;
step 6: calculating a toughness evaluation index value R under the typhoon disaster scene 1 by using a formula (1-2) and the fault probability of each power transmission branch under the typhoon disaster scene 1 1 ；
And 7: calculating toughness evaluation index value R of 1 in typhoon disaster scene 1 Partial derivatives of order N;
and step 8: let w be w + 1;
and step 9: calculating toughness evaluation index value R under typhoon disaster scene w according to fault probability of each power transmission branch under typhoon disaster scene w w ；
Step 10: if W is less than W, go to step 8; otherwise, go to step 11;
step 11: calculating a toughness index R of the power transmission system considering typhoon uncertainty by using a formula (1-3) and the occurrence probability of each typhoon disaster scene;
wherein phi W Representing a set of typhoon disaster scenes; p w Representing the occurrence probability of a certain typhoon disaster scene w; n represents the fault state order of the toughness evaluation index to be considered; omega n Is an n-order fault state set under typhoon disaster w; p is a radical of formula wm Representing the fault probability of the mth power transmission branch in the fault state s caused by the typhoon disaster scene w; wherein:
in the step 9, the index R is evaluated according to the system toughness in the typhoon disaster scene 1 According to the result, the toughness evaluation index R of the power transmission system under the typhoon disaster weather w is obtained through the formula (1-4) w Namely:
wherein p is 1 ＝[p 11 ,…,p 1i ,…,p 1M ]Representing a vector formed by fault probabilities of all power transmission branches under typhoon disaster weather obtained by first simulation; Δ p w ＝[Δp w1 ,…,Δp wi ,…,Δp wM ]And representing a vector formed by the fault probability of each power transmission branch in the typhoon disaster scene w obtained by simulation and the change value of the fault probability of each power transmission branch in the typhoon disaster weather obtained by first simulation.
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| CN112288326A (en) * | 2020-11-23 | 2021-01-29 | 天津大学 | Fault scene set reduction method suitable for toughness evaluation of power transmission system |
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