CN103985059B

CN103985059B - Power grid transformer operational risk assessment method based on fuzzy fault rate

Info

Publication number: CN103985059B
Application number: CN201410158406.2A
Authority: CN
Inventors: 吴文传; 张伯明; 孙宏斌; 郭昆亚; 宁辽逸; 王英男; 汲国强; 黄哲洙; 郭庆来
Original assignee: Tsinghua University; State Grid Corp of China SGCC; Shenyang Power Supply Co of State Grid Liaoning Electric Power Co Ltd
Current assignee: Tsinghua University; State Grid Corp of China SGCC; Shenyang Power Supply Co of State Grid Liaoning Electric Power Co Ltd
Priority date: 2014-04-18
Filing date: 2014-04-18
Publication date: 2017-01-18
Anticipated expiration: 2034-04-18
Also published as: CN103985059A

Abstract

The invention relates to a power grid transformer operational risk assessment method based on a fuzzy fault rate, and belongs to the field of operational risk assessment of an electric power system. According to the power grid transformer operational risk assessment method, various operational states of a transformer are divided, a transformer sudden failure rate and ageing fault rate represented in a triangular fuzzy number mode are given, a transformer Markov state transition differential equation set based on the fuzzy fault rate is established to describe the state transition behavior of the transformer, the transformer state transition differential equation set is solved through Laplace transformation, a transformer availability analysis formula based on the fuzzy failure rate is given out, the probability of a power grid in various operation modes is calculated based on the transformer availability analysis formula, and at last the transformer operational risk indicators of the power grid at all moments are calculated. The power grid transformer operational risk assessment method can be used for conducting power grid transformer operational risk assessment under the condition that historical statistical data are insufficient, by the aid of manual experience, an optimistic value, a pessimistic value and an intermediate value of the power grid transformer operational risk indicators are given, and therefore more sufficient decision support is provided for scheduling personnel.

Description

A risk assessment method for power grid transformer operation based on fuzzy failure rate

技术领域technical field

本发明涉及一种基于模糊故障率的电网变压器运行风险评估方法，属于电力系统运行风险评估领域。The invention relates to a method for assessing the operation risk of a power grid transformer based on a fuzzy failure rate, and belongs to the field of electric system operation risk assessment.

背景技术Background technique

风险是事件发生可能性和严重性的综合度量，电网运行风险评估可以综合考虑电网运行中所发生故障的严重程度和发生概率，从而揭示电网薄弱环节，给电网调度人员决策提供参考依据。Risk is a comprehensive measurement of the possibility and severity of events. Grid operation risk assessment can comprehensively consider the severity and probability of faults in grid operation, thereby revealing the weak links of the grid and providing reference for grid dispatchers to make decisions.

在传统电网运行风险评估中，故障发生可能性的计算主要取决于电力设备故障率参数，而设备故障率参数主要来源于长期历史统计数据或设备生产厂商提供的参考值，这一方法目前面临以下问题：In the traditional power grid operation risk assessment, the calculation of the possibility of failure mainly depends on the failure rate parameters of power equipment, and the failure rate parameters of equipment mainly come from long-term historical statistical data or reference values provided by equipment manufacturers. This method currently faces the following problems: question:

1、由于设备发生故障的可能性极低，故障率数据统计周期极为漫长，这就导致许多地区电网中电力设备历史统计数据样本较少，难以准确计算设备故障率；1. Due to the extremely low possibility of equipment failure, the statistical cycle of failure rate data is extremely long, which leads to fewer historical statistical data samples of power equipment in power grids in many regions, making it difficult to accurately calculate the equipment failure rate;

2、在一些基础设施较为薄弱的地区配电网中，由于设施落后、资金短缺或人力不足等原因，许多设备缺乏历史统计数据，无法计算设备故障率；2. In distribution networks in some areas with relatively weak infrastructure, due to backward facilities, shortage of funds or insufficient manpower, many equipment lack historical statistical data, and the failure rate of equipment cannot be calculated;

3、设备故障率通常会随设备运行工况和外界环境而变化，存在一个波动区间，而设备生产厂商提供的故障率参考值，难以反映设备所处的实际运行工况和外部环境等因素，因此准确性较差。3. The failure rate of equipment usually changes with the operating conditions of the equipment and the external environment, and there is a fluctuation range. However, the reference value of the failure rate provided by the equipment manufacturer cannot reflect the actual operating conditions of the equipment and the external environment. So less accurate.

发明内容Contents of the invention

本发明的目的是提出一种基于模糊故障率的电网变压器运行风险评估方法，给出了三角模糊数形式表示的变压器突发故障率和老化故障率，并建立了基于模糊故障率的变压器马尔可夫状态转移微分方程组，通过求解变压器状态转移微分方程组得到变压器可用度解析式，并基于变压器可用度解析式计算电网各个时刻的变压器运行风险指标。The purpose of the present invention is to propose a method for evaluating the risk of power grid transformer operation based on fuzzy failure rate, which provides the sudden failure rate and aging failure rate of transformers expressed in the form of triangular fuzzy numbers, and establishes a transformer Markov based on fuzzy failure rate. The transformer state transition differential equations are solved, and the transformer availability analytical formula is obtained by solving the transformer state transition differential equations, and based on the transformer availability analytical formula, the transformer operation risk index at each moment of the power grid is calculated.

本发明提出的基于模糊故障率的电网变压器运行风险评估方法，包括以下步骤：The fuzzy fault rate-based grid transformer operation risk assessment method proposed by the present invention comprises the following steps:

（1）将变压器的状态划分为工作状态和故障状态，其中工作状态包括正常、注意和异常，分别记为0、1和2，故障状态根据故障原因细分为突发故障和老化故障，分别记为3和4；(1) The state of the transformer is divided into working state and fault state, where the working state includes normal, attention and abnormal, which are recorded as 0, 1 and 2 respectively, and the fault state is subdivided into sudden fault and aging fault according to the cause of the fault, respectively Denote as 3 and 4;

（2）分别用和和表示变压器在正常、注意和异常状态下的突发故障率，用表示变压器的老化故障率，用如下所示的三角模糊数形式表示突发故障率和老化故障率：(2) use respectively And and Indicates the sudden failure rate of the transformer in normal, attention and abnormal state, using Indicates the aging failure rate of the transformer, and expresses the sudden failure rate and aging failure rate in the form of triangular fuzzy numbers as shown below:

${\overset{~ ~}{λ λ}}_{0303} = = (({\underset{&OverBar; &OverBar;}{λ λ}}_{0303},, {\overset{^^}{λ λ}}_{0303},, {\overset{&OverBar; &OverBar;}{λ λ}}_{0303}))$

${\overset{~ ~}{λ λ}}_{1313} = = (({\underset{&OverBar; &OverBar;}{λ λ}}_{1313},, {\overset{^^}{λ λ}}_{1313},, {\overset{&OverBar; &OverBar;}{λ λ}}_{1313}))$

${\overset{~ ~}{λ λ}}_{23 twenty three} = = (({\underset{&OverBar; &OverBar;}{λ λ}}_{23 twenty three},, {\overset{^^}{λ λ}}_{23 twenty three},, {\overset{&OverBar; &OverBar;}{λ λ}}_{23 twenty three}))$

${\overset{~ ~}{λ λ}}_{24 twenty four} = = (({\underset{&OverBar; &OverBar;}{λ λ}}_{24 twenty four},, {\overset{^^}{λ λ}}_{24 twenty four},, {\overset{&OverBar; &OverBar;}{λ λ}}_{24 twenty four}))$

其中λ ₀₃、λ ₁₃和λ ₂₃分别表示变压器在正常、注意和异常状态下的突发故障率的下限值，和分别表示变压器在正常、注意和异常状态下的突发故障率上限值，和分别表示变压器在正常、注意和异常状态下的突发故障率中间值，λ ₂₄表示变压器的老化故障率下限值，表示变压器的老化故障率上限值，表示变压器的老化故障率中间值；下限值为调度人员基于经验给出的故障率乐观估计值，取值范围为0～0.005次/天，上限值为调度人员基于经验给出的故障率悲观估计值，取值范围为0～0.1次/天，中间值为调度人员基于经验和变压器当前运行工况给出的实际估计值，取值范围为0～0.01次/天。Among them, λ ₀₃ , λ ₁₃ and λ ₂₃ represent the lower limit of the sudden failure rate of the transformer in normal state, attention state and abnormal state respectively, and Respectively represent the upper limit of the sudden failure rate of the transformer in the normal state, attention state and abnormal state, and Respectively represent the middle value of the sudden failure rate of the transformer under normal, attention and abnormal state, λ ₂₄ represents the lower limit value of the aging failure rate of the transformer, Indicates the upper limit of the aging failure rate of the transformer, Indicates the intermediate value of the aging failure rate of the transformer; the lower limit is the optimistic estimate of the failure rate given by the dispatcher based on experience, and the value range is 0 to 0.005 times/day, and the upper limit is the failure rate given by the dispatcher based on experience The pessimistic estimated value ranges from 0 to 0.1 times/day, and the median value is the actual estimated value given by the dispatcher based on experience and the current operating conditions of the transformer, and the value range is 0 to 0.01 times/day.

（3）建立一个如下所示的变压器马尔可夫状态转移微分方程组：(3) Establish a transformer Markov state transition differential equation system as shown below:

$\{\begin{matrix} \frac{d d {\overset{~ ~}{P P}}_{00}}{dt dt} = = - - (({λ λ}_{0101} + + {\overset{~ ~}{λ λ}}_{0303})) {\overset{~ ~}{P P}}_{00} + + {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.0 3.0} + + {μ μ}_{c c} {\overset{~ ~}{P P}}_{44} \\ \frac{d d {\overset{~ ~}{P P}}_{11}}{dt dt} = = {λ λ}_{0101} {\overset{~ ~}{P P}}_{00} - - (({λ λ}_{1212} + + {\overset{~ ~}{λ λ}}_{1313})) {\overset{~ ~}{P P}}_{11} + + {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.2 3.2} \\ \frac{d d {\overset{~ ~}{P P}}_{22}}{dt dt} = = {λ λ}_{1212} {\overset{~ ~}{P P}}_{11} - - (({\overset{~ ~}{λ λ}}_{23 twenty three} + + {\overset{~ ~}{λ λ}}_{24 twenty four})) {\overset{~ ~}{P P}}_{22} + + {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.2 3.2} \\ \frac{d d {\overset{~ ~}{P P}}_{3.2 3.2}}{dt dt} = = {\overset{~ ~}{λ λ}}_{23 twenty three} {\overset{~ ~}{P P}}_{22} - - {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.2 3.2} \\ \frac{d d {\overset{~ ~}{P P}}_{3.1 3.1}}{dt dt} = = {\overset{~ ~}{λ λ}}_{1313} {\overset{~ ~}{P P}}_{11} - - {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.1 3.1} \\ \frac{d d {\overset{~ ~}{P P}}_{3.0 3.0}}{dt dt} = = {\overset{~ ~}{λ λ}}_{0303} {\overset{~ ~}{P P}}_{00} - - {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.0 3.0} \\ \frac{d d {\overset{~ ~}{P P}}_{44}}{dt dt} = = {\overset{~ ~}{λ λ}}_{24 twenty four} {\overset{~ ~}{P P}}_{22} - - {μ μ}_{c c} {\overset{~ ~}{P P}}_{44} \end{matrix}$

其中，λ₀₁表示变压器由正常状态到注意状态的转移速率，λ₁₂表示变压器由注意状态到异常状态的转移速率，μ_c表示变压器老化故障的修复率，取值范围为0～1次/天，μ_b表示变压器突发故障的修复率，取值范围为0～10次/天，和分别表示变压器处于正常、注意和异常状态的概率，表示变压器处于老化故障状态的概率，表示变压器处于突发故障状态且发生故障前变压器处于正常状态的概率，表示变压器处于突发故障状态且发生故障前变压器处于注意状态的概率，表示变压器处于突发故障状态且发生故障前变压器处于异常状态的概率；Among them, λ ₀₁ represents the transition rate of the transformer from the normal state to the attention state, λ ₁₂ represents the transfer rate of the transformer from the attention state to the abnormal state, μ _c represents the repair rate of the transformer aging fault, and the value range is 0 to 1 time/day , μ _b represents the recovery rate of sudden transformer faults, the value range is 0-10 times/day, and represent the probability that the transformer is in normal state, attention state and abnormal state respectively, Indicates the probability that the transformer is in an aging fault state, Indicates the probability that the transformer is in a sudden fault state and the transformer is in a normal state before the fault occurs, Indicates the probability that the transformer is in a state of sudden fault and the transformer is in the attention state before the fault occurs, Indicates the probability that the transformer is in a sudden fault state and the transformer is in an abnormal state before the fault occurs;

（4）根据马尔可夫状态转移微分方程组，得到变压器的可用度解析式，具体过程包括以下步骤：(4) According to the Markov state transition differential equations, the analytical formula of transformer availability is obtained. The specific process includes the following steps:

（4-1）设变压器初始化时处于正常状态，采用拉氏变换，将上述微分方程组转化成如下代数方程组：(4-1) Assuming that the transformer is in a normal state when it is initialized, the above differential equations are transformed into the following algebraic equations by using Laplace transform:

$\{\begin{matrix} s the s {\overset{~ ~}{P P}}_{00} - - 11 = = - - (({λ λ}_{0101} + + {\overset{~ ~}{λ λ}}_{0303})) {\overset{~ ~}{P P}}_{00} + + {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.0 3.0} + + {μ μ}_{c c} {\overset{~ ~}{P P}}_{44} \\ s the s {\overset{~ ~}{P P}}_{11} = = {λ λ}_{0101} {\overset{~ ~}{P P}}_{00} - - (({λ λ}_{1212} + + {\overset{~ ~}{λ λ}}_{1313})) {\overset{~ ~}{P P}}_{11} + + {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.1 3.1} \\ s the s {\overset{~ ~}{P P}}_{22} = = {λ λ}_{1212} {\overset{~ ~}{P P}}_{11} - - (({\overset{~ ~}{λ λ}}_{23 twenty three} + + {\overset{~ ~}{λ λ}}_{24 twenty four})) {\overset{~ ~}{P P}}_{22} + + {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.2 3.2} \\ s the s {\overset{~ ~}{P P}}_{3.2 3.2} = = {\overset{~ ~}{λ λ}}_{23 twenty three} {\overset{~ ~}{P P}}_{22} - - {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.2 3.2} \\ s the s {\overset{~ ~}{P P}}_{3.1 3.1} = = {\overset{~ ~}{λ λ}}_{1313} {\overset{~ ~}{P P}}_{11} - - {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.1 3.1} \\ s the s {\overset{~ ~}{P P}}_{3.0 3.0} = = {\overset{~ ~}{λ λ}}_{0303} {\overset{~ ~}{P P}}_{00} - - {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.0 3.0} \\ s the s {\overset{~ ~}{P P}}_{44} = = {\overset{~ ~}{λ λ}}_{24 twenty four} {\overset{~ ~}{P P}}_{22} - - {μ μ}_{c c} {\overset{~ ~}{P P}}_{44} \end{matrix}$

其中，s为拉氏变换中的复频率，拉氏变换是将时域内的函数变换到复频域内的复变函数的一个积分变换过程；Among them, s is the complex frequency in the Laplace transform, and the Laplace transform is an integral transformation process that transforms a function in the time domain into a complex variable function in the complex frequency domain;

（4-2）以拉氏变换复频率s为自变量，以变压器处于正常、注意和异常状态的概率和为因变量，将和与s的关系以如下标准形式表达：(4-2) Take the Laplace transform complex frequency s as the independent variable, and take the probability that the transformer is in normal, attention and abnormal state and as the dependent variable, will and The relation to s is expressed in the standard form as follows:

${\overset{~ ~}{P P}}_{00} ((s the s)) = = {Σ Σ}_{i i = = 00}^{66} \frac{{\overset{~ ~}{L L}}_{00 i i}}{s the s - - {\overset{~ ~}{s the s}}_{i i}}$

${\overset{~ ~}{P P}}_{11} ((s the s)) = = {Σ Σ}_{i i = = 11}^{88} \frac{{\overset{~ ~}{L L}}_{11 i i}}{s the s - - {\overset{~ ~}{s the s}}_{i i}}$

${\overset{~ ~}{P P}}_{22} ((s the s)) = = {Σ Σ}_{i i = = 11}^{1010} \frac{{\overset{~ ~}{L L}}_{22 i i}}{s the s - - {\overset{~ ~}{s the s}}_{i i}}$

其中和为标准形式中的中间系数，通常为复数，其模的取值范围通常为0～1；in and is the intermediate coefficient in the standard form, usually a complex number, and its modulus usually ranges from 0 to 1;

（4-3）将上述标准形式进行拉氏反变换，得到变压器在t时刻处于正常、注意和异常状态的概率的时域解析表达式如下：(4-3) Perform inverse Laplace transform on the above standard form to obtain the time-domain analytical expression of the probability that the transformer is in the normal, attention and abnormal states at time t as follows:

${\overset{~ ~}{P P}}_{00} = = {Σ Σ}_{i i = = 00}^{66} {\overset{~ ~}{L L}}_{00 i i} {e e}^{{\overset{~ ~}{s the s}}_{i i} t t}$

${\overset{~ ~}{P P}}_{11} = = {Σ Σ}_{i i = = 11}^{88} {\overset{~ ~}{L L}}_{11 i i} {e e}^{{\overset{~ ~}{s the s}}_{i i} t t}$

${\overset{~ ~}{P P}}_{22} = = {Σ Σ}_{i i = = 11}^{1010} {\overset{~ ~}{L L}}_{22 i i} {e e}^{{\overset{~ ~}{s the s}}_{i i} t t}$

（4-4）根据步骤（4-3）的时域解析表达式，得到变压器在t时刻的可用度解析式如下：(4-4) According to the time-domain analytical expression in step (4-3), the availability of the transformer at time t is obtained The analytical formula is as follows:

$\overset{~ ~}{A A} ((t t)) = = {\overset{~ ~}{P P}}_{00} + + {\overset{~ ~}{P P}}_{11} + + {\overset{~ ~}{P P}}_{22} = = {Σ Σ}_{i i = = 00}^{66} {\overset{~ ~}{L L}}_{00 i i} {e e}^{{\overset{~ ~}{s the s}}_{i i} t t} + + {Σ Σ}_{i i = = 11}^{88} {\overset{~ ~}{L L}}_{11 i i} {e e}^{{\overset{~ ~}{s the s}}_{i i} t t} + + {Σ Σ}_{i i = = 11}^{1010} {\overset{~ ~}{L L}}_{22 i i} {e e}^{{\overset{~ ~}{s the s}}_{i i} t t};;$

（5）将上述变压器在t时刻的可用度表示为三角模糊数形式如下：(5) The availability of the above transformer at time t Expressed as a triangular fuzzy number, the form is as follows:

$\overset{~ ~}{A A} ((t t)) = = ((\underset{&OverBar; &OverBar;}{A A} ((t t)),, \overset{^^}{A A} ((t t)),, \overset{&OverBar; &OverBar;}{A A} ((t t))))$

其中A(t)表示变压器在t时刻的可用度下限值，表示变压器在t时刻的可用度上限值，表示变压器在t时刻的可用度中间值，下限值、上限值和中间值的求解过程如下：where A (t) represents the lower limit of transformer availability at time t, Indicates the upper limit of the availability of the transformer at time t, Indicates the intermediate value of transformer availability at time t, and the solution process of the lower limit, upper limit and intermediate value is as follows:

（5-1）用上述步骤（2）的变压器突发故障率的上限值和代替步骤（3）马尔可夫状态转移微分方程组中的突发故障率和用步骤（2）的变压器老化故障率的上限值代替步骤（3）马尔可夫状态转移微分方程组中的老化故障率执行步骤（4-1）～步骤（4-4），得到变压器在t时刻的可用度下限值A(t)；(5-1) The upper limit value of the sudden failure rate of the transformer using the above step (2) and Instead of step (3) the burst failure rate in the Markov state transition differential equation system and Upper limit of transformer aging failure rate using step (2) Instead of step (3) aging failure rate in the Markov state transition differential equation system Execute steps (4-1) to (4-4) to obtain the lower limit value A (t) of transformer availability at time t;

（5-2）用上述步骤（2）的变压器突发故障率的下限值λ ₀₃、λ ₁₃和λ ₂₃代替步骤（3）马尔可夫状态转移微分方程组中的突发故障率和用步骤（2）的变压器老化故障率的下限值代替步骤（3）马尔可夫状态转移微分方程组中的老化故障率执行步骤（4-1）～步骤（4-4），得到变压器在t时刻的可用度的上限值 (5-2) Use the lower limit values λ ₀₃ , λ ₁₃ and λ ₂₃ of the transformer sudden failure rate in the above step (2) to replace the sudden failure rate in the Markov state transition differential equations in step (3) and The lower limit value of transformer aging failure rate using step (2) Instead of step (3) aging failure rate in the Markov state transition differential equation system Execute steps (4-1) to (4-4) to obtain the upper limit of transformer availability at time t

（5-3）用上述步骤（2）的变压器突发故障率的中间值和代替步骤（3）马尔可夫状态转移微分方程组中的突发故障率和用步骤（2）的变压器老化故障率的中间值代替步骤（3）马尔可夫状态转移微分方程组中的老化故障率执行步骤（4-1）～步骤（4-4），得到变压器在t时刻的可用度的中间值 (5-3) Median value of transformer sudden failure rate using the above step (2) and Instead of step (3) the burst failure rate in the Markov state transition differential equation system and The median value of transformer aging failure rate using step (2) Instead of step (3) aging failure rate in the Markov state transition differential equation system Execute steps (4-1) to (4-4) to obtain the intermediate value of transformer availability at time t

（6）设电网在t时刻处于一种运行状态的概率为：(6) Suppose the probability that the power grid is in a running state at time t for:

$\overset{~ ~}{P P} ((t t)) = = \underset{i i &Element; &Element; {S S}_{on on}}{Π Π} {\overset{~ ~}{A A}}_{i i} ((t t)) \underset{i i &Element; &Element; {S S}_{off off}}{Π Π} ((11 - - {\overset{~ ~}{A A}}_{i i} ((t t))))$

其中，S_on表示电网在该运行状态下处于工作状态的变压器集合，S_off表示电网在该运行状态下处于故障状态的变压器集合，下标i表示变压器编号，表示第i台变压器在t时刻的可用度；Among them, S _on represents the set of transformers in the working state of the power grid in this operating state, S _off represents the set of transformers in the fault state of the power grid in this operating state, and the subscript i represents the transformer number, Indicates the availability of the i-th transformer at time t;

（7）设对电网变压器进行运行风险评估的时间长度为T，电网中共有N台变压器，计算电网变压器运行风险指标的过程如下：(7) Assuming that the time length for the operation risk assessment of the power grid transformer is T, there are N transformers in the power grid, and the operation risk index of the power grid transformer is calculated The process is as follows:

（7-1）初始化时，设时刻t＝0；(7-1) When initializing, set time t=0;

（7-2）使t＝t+1，将电网t时刻变压器运行风险指标表示成三角模糊数形式如下：(7-2) Let t=t+1, the transformer operation risk index of power grid at time t It is expressed as a triangular fuzzy number as follows:

$\overset{~ ~}{R R} ((t t)) = = ((\underset{&OverBar; &OverBar;}{R R} ((t t)),, \overset{^^}{R R} ((t t)),, \overset{&OverBar; &OverBar;}{R R} ((t t))))$

其中R(t)表示电网在t时刻变压器运行风险指标的下限值，表示电网在t时刻变压器运行风险指标的上限值，表示电网在t时刻变压器运行风险指标的中间值，分别计算电网在t时刻变压器运行风险指标的上限值、下限值和中间值如下：Where R (t) represents the lower limit value of the transformer operation risk index of the power grid at time t, Indicates the upper limit value of the transformer operation risk index of the power grid at time t, Indicates the median value of the transformer operation risk index of the power grid at time t, and the upper limit, lower limit and middle value of the transformer operation risk index of the power grid at time t are calculated as follows:

（7-2-1）列举t时刻电网的所有运行状态，根据电网运行状态，分别确定每种运行状态下处于工作状态的变压器集合S_on和处于故障状态的变压器集合S_off；(7-2-1) Enumerate all the operating states of the power grid at time t, and determine the transformer set S _on in the working state and the transformer set S _off in the fault state in each operating state according to the operating state of the power grid;

（7-2-2）利用电网潮流计算方法，计算电网在每一种运行状态下的失负荷量S_j(t)，下标j为该运行状态的编号；(7-2-2) Use the grid power flow calculation method to calculate the load loss S _j (t) of the grid in each operating state, and the subscript j is the number of the operating state;

（7-2-3）对电网的每种运行状态，用步骤（5）的各台变压器可用度上限值代替步骤（6）中的变压器可用度利用步骤（6）的公式进行计算，将计算结果记为利用下式计算得到t时刻电网变压器运行风险指标的下限值：(7-2-3) For each operating state of the power grid, use the upper limit of the availability of each transformer in step (5) Instead of transformer availability in step (6) Use the formula in step (6) to calculate, and record the calculation result as Use the following formula to calculate the lower limit value of the grid transformer operation risk index at time t:

$\underset{&OverBar; &OverBar;}{R R} ((t t)) = = {Σ Σ}_{j j = = 11}^{22^{N N}} {\overset{&OverBar; &OverBar;}{P P}}_{j j} ((t t)) \cdot \cdot {S S}_{j j} ((t t));;$

（7-2-4）对电网的每种运行状态，用步骤（5）的各台变压器可用度下限值A(t)代替步骤（6）中的变压器可用度利用步骤（6）的公式进行计算，将计算结果记为P _j(t)，利用下式计算得到t时刻电网变压器运行风险指标的上限值：(7-2-4) For each operating state of the power grid, replace the transformer availability in step (6) with the lower limit value A(t) of each transformer availability in step (5) Use the formula in step (6) to calculate, record the calculation result as P _j (t), and use the following formula to calculate the upper limit value of the grid transformer operation risk index at time t:

$\overset{&OverBar; &OverBar;}{R R} ((t t)) = = {Σ Σ}_{j j = = 11}^{22^{N N}} {\underset{&OverBar; &OverBar;}{P P}}_{j j} ((t t)) \cdot \cdot {S S}_{j j} ((t t));;$

（7-2-5）对电网的每种运行状态，用步骤（5）的各台变压器可用度中间值代替步骤（6）中的变压器可用度利用步骤（6）的公式进行计算，将计算结果记为利用下式计算得到t时刻电网变压器运行风险指标的中间值：(7-2-5) For each operating state of the power grid, use the median value of the availability of each transformer in step (5) Instead of transformer availability in step (6) Use the formula in step (6) to calculate, and record the calculation result as Use the following formula to calculate the median value of the grid transformer operation risk index at time t:

$\overset{^^}{R R} ((t t)) = = {Σ Σ}_{j j = = 11}^{22^{N N}} {\overset{^^}{P P}}_{j j} ((t t)) \cdot \cdot {S S}_{j j} ((t t));;$

（7-3）对时刻t进行判断，若t＜T，则返回步骤（7-2），若t=T，则以上述步骤（7-2）的作为电网变压器运行风险指标。(7-3) Judging the time t, if t<T, then return to step (7-2), if t=T, then use the above step (7-2) As a power grid transformer operation risk indicator.

本发明提出的一种基于模糊故障率的电网变压器运行风险评估方法，其优点是：本发明方法借鉴人工经验，用三角模糊数形式表示变压器突发故障率和老化故障率，给出了基于模糊故障率的变压器可用度解析式，通过借鉴人工经验，有效弥补了历史统计数据不足的缺陷，解决了传统方法在历史统计数据不足情况下难以准确计算电网运行风险指标这一问题，并且，该方法通过给出电网变压器运行风险指标的乐观值、悲观值和中间值，可以更加准确的反应电网运行中存在的薄弱环节，从而给电网调度人员提供更充分的决策支持。A fuzzy failure rate-based power grid transformer operation risk assessment method proposed by the present invention has the advantages that: the method of the present invention draws on manual experience, expresses the sudden failure rate and aging failure rate of transformers in the form of triangular fuzzy numbers, and gives a fuzzy-based The transformer availability analysis formula of failure rate, by drawing on manual experience, effectively makes up for the shortcomings of insufficient historical statistical data, and solves the problem that traditional methods are difficult to accurately calculate power grid operation risk indicators when historical statistical data is insufficient. Moreover, this method By giving the optimistic value, pessimistic value and intermediate value of the power grid transformer operation risk index, it can more accurately reflect the weak links in the power grid operation, so as to provide more sufficient decision support for the power grid dispatcher.

具体实施方式detailed description

（1）将变压器的状态划分为工作状态和故障状态，其中工作状态包括正常、注意和异常，分别记为0、1和2，故障状态根据故障原因细分为突发故障和老化故障，分别记为3和4；(1) Divide the state of the transformer into working state and fault state, where the working state includes normal, attention and abnormal, which are recorded as 0, 1 and 2 respectively, and the fault state is subdivided into sudden fault and aging fault according to the cause of the fault, respectively Denote as 3 and 4;

（2）分别用和表示变压器在正常、注意和异常状态下的突发故障率，用表示变压器的老化故障率，用如下所示的三角模糊数形式表示突发故障率和老化故障率：(2) use respectively and Indicates the sudden failure rate of the transformer in normal, attention and abnormal state, using Indicates the aging failure rate of the transformer, and expresses the sudden failure rate and aging failure rate in the form of triangular fuzzy numbers as shown below:

（5-2）用上述步骤（2）的变压器突发故障率的下限值λ ₀₃、λ ₁₃和λ ₂₃代替步骤（3）马尔可夫状态转移微分方程组中的突发故障率和用步骤（2）的变压器老化故障率的下限值λ ₂₄代替步骤（3）马尔可夫状态转移微分方程组中的老化故障率执行步骤（4-1）～步骤（4-4），得到变压器在t时刻的可用度的上限值 (5-2) Use the lower limit values λ ₀₃ , λ ₁₃ and λ ₂₃ of the transformer sudden failure rate in the above step (2) to replace the sudden failure rate in the Markov state transition differential equations in step (3) and Replace the aging failure rate in the step (3) Markov state transition differential equations with the lower limit value λ ₂₄ of the transformer aging failure rate in step (2) Execute steps (4-1) to (4-4) to obtain the upper limit of transformer availability at time t

（7-1）初始化时，设时刻t＝0；(7-1) When initializing, set time t=0;

$\underset{&OverBar; &OverBar;}{R R} ((t t)) = = {Σ Σ}_{j j = = 11}^{22^{N N}} {\overset{&OverBar; &OverBar;}{P P}}_{j j} ((t t)) \cdot &Center Dot; {S S}_{j j} ((t t));;$

（7-2-4）对电网的每种运行状态，用步骤（5）的各台变压器可用度下限值A(t)代替步骤（6）中的变压器可用度利用步骤（6）的公式进行计算，将计算结果记为P _j(t)，利用下式计算得到t时刻电网变压器运行风险指标的上限值：(7-2-4) For each operating state of the power grid, replace the transformer availability in step (6) with the lower limit value A (t) of each transformer availability in step (5) Use the formula in step (6) to calculate, record the calculation result as P _j (t), and use the following formula to calculate the upper limit value of the grid transformer operation risk index at time t:

$\overset{&OverBar; &OverBar;}{R R} ((t t)) = = {Σ Σ}_{j j = = 11}^{22^{N N}} {\underset{&OverBar; &OverBar;}{P P}}_{j j} ((t t)) \cdot &Center Dot; {S S}_{j j} ((t t));;$

$\overset{^^}{R R} ((t t)) = = {Σ Σ}_{j j = = 11}^{22^{N N}} {\overset{^^}{P P}}_{j j} ((t t)) \cdot &Center Dot; {S S}_{j j} ((t t));;$

Claims

1. A method for assessing the risk of power grid transformer operation based on fuzzy failure rate, characterized in that the method comprises the following steps:

(1) Divide the state of the transformer into working state and fault state, where the working state includes normal, attention and abnormal, which are recorded as 0, 1 and 2 respectively, and the fault state is subdivided into sudden fault and aging fault according to the cause of the fault, respectively Denote as 3 and 4;

(2) use respectively and Indicates the sudden failure rate of the transformer in normal, attention and abnormal state, using Indicates the aging failure rate of the transformer, and expresses the sudden failure rate and aging failure rate in the form of triangular fuzzy numbers as shown below:

{\overset{~ ~}{λ λ}}_{0303} = = (({\underset{&OverBar; &OverBar;}{λ λ}}_{0303},, {\overset{^^}{λ λ}}_{0303},, {\overset{&OverBar; &OverBar;}{λ λ}}_{0303}))

{\overset{~ ~}{λ λ}}_{1313} = = (({\underset{&OverBar; &OverBar;}{λ λ}}_{1313},, {\overset{~ ~}{λ λ}}_{1313},, {\overset{&OverBar; &OverBar;}{λ λ}}_{1313}))

{\overset{~ ~}{λ λ}}_{23 twenty three} = = (({\underset{&OverBar; &OverBar;}{λ λ}}_{23 twenty three},, {\overset{~ ~}{λ λ}}_{23 twenty three},, {\overset{&OverBar; &OverBar;}{λ λ}}_{23 twenty three}))

{\overset{~ ~}{λ λ}}_{24 twenty four} = = (({\underset{&OverBar; &OverBar;}{λ λ}}_{24 twenty four},, {\overset{~ ~}{λ λ}}_{24 twenty four},, {\overset{&OverBar; &OverBar;}{λ λ}}_{24 twenty four}))

Among them, λ ₀₃ , λ ₁₃ and λ ₂₃ represent the lower limit of the sudden failure rate of the transformer in normal state, attention state and abnormal state respectively, and Respectively represent the upper limit of the sudden failure rate of the transformer in the normal state, attention state and abnormal state, and Respectively represent the middle value of the sudden failure rate of the transformer under normal, attention and abnormal state, λ ₂₄ represents the lower limit value of the aging failure rate of the transformer, Indicates the upper limit of the aging failure rate of the transformer, Indicates the intermediate value of the aging failure rate of the transformer; the lower limit is the optimistic estimate of the failure rate given by the dispatcher based on experience, and the value range is 0 to 0.005 times/day, and the upper limit is the failure rate given by the dispatcher based on experience The pessimistic estimated value ranges from 0 to 0.1 times/day, and the median value is the actual estimated value given by the dispatcher based on experience and the current operating conditions of the transformer, and the value range is 0 to 0.01 times/day;

(3) Establish a transformer Markov state transition differential equation system as shown below:

\{\begin{matrix} \frac{d d {\overset{~ ~}{P P}}_{00}}{d d t t} = = - - (({λ λ}_{0101} + + {\overset{~ ~}{λ λ}}_{0303})) {\overset{~ ~}{P P}}_{00} + + {μ μ}_{00} {\overset{~ ~}{P P}}_{3.0 3.0} + + {μ μ}_{c c} {\overset{~ ~}{P P}}_{44} \\ \frac{d d {\overset{~ ~}{P P}}_{11}}{d d t t} = = {λ λ}_{0101} {\overset{~ ~}{P P}}_{00} - - (({λ λ}_{1212} + + {\overset{~ ~}{λ λ}}_{1313})) {\overset{~ ~}{P P}}_{11} + + {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.1 3.1} \\ \frac{d d {\overset{~ ~}{P P}}_{22}}{d d t t} = = {λ λ}_{1212} {\overset{~ ~}{P P}}_{11} - - (({\overset{~ ~}{λ λ}}_{23 twenty three} + + {\overset{~ ~}{λ λ}}_{24 twenty four})) {\overset{~ ~}{P P}}_{22} + + {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.2 3.2} \\ \frac{d d {\overset{~ ~}{P P}}_{3.2 3.2}}{d d t t} = = {\overset{~ ~}{λ λ}}_{23 twenty three} {\overset{~ ~}{P P}}_{22} - - {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.2 3.2} \\ \frac{d d {\overset{~ ~}{P P}}_{3.1 3.1}}{d d t t} = = {\overset{~ ~}{λ λ}}_{1313} {\overset{~ ~}{P P}}_{11} - - {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.1 3.1} \\ \frac{d d {\overset{~ ~}{P P}}_{3.0 3.0}}{d d t t} = = {\overset{~ ~}{λ λ}}_{0303} {\overset{~ ~}{P P}}_{00} - - {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.0 3.0} \\ \frac{d d {\overset{~ ~}{P P}}_{44}}{d d t t} = = {\overset{~ ~}{λ λ}}_{24 twenty four} {\overset{~ ~}{P P}}_{22} - - {μ μ}_{c c} {\overset{~ ~}{P P}}_{44} \end{matrix}

Among them, λ ₀₁ represents the transition rate of the transformer from the normal state to the attention state, λ ₁₂ represents the transfer rate of the transformer from the attention state to the abnormal state, μ _c represents the repair rate of the transformer aging fault, and the value range is 0 to 1 time/day , μ _b represents the recovery rate of sudden transformer faults, the value range is 0-10 times/day, and represent the probability that the transformer is in normal state, attention state and abnormal state respectively, Indicates the probability that the transformer is in an aging fault state, Indicates the probability that the transformer is in a sudden fault state and the transformer is in a normal state before the fault occurs, Indicates the probability that the transformer is in a state of sudden fault and the transformer is in the attention state before the fault occurs, Indicates the probability that the transformer is in a sudden fault state and the transformer is in an abnormal state before the fault occurs;

(4) According to the Markov state transition differential equations, the analytical formula of transformer availability is obtained. The specific process includes the following steps:

(4-1) Assuming that the transformer is in a normal state when it is initialized, the above differential equations are converted into the following algebraic equations by using Laplace transform:

\{\begin{matrix} s the s {\overset{~ ~}{P P}}_{00} - - 11 = = - - (({λ λ}_{0101} + + {\overset{~ ~}{λ λ}}_{0303})) {\overset{~ ~}{P P}}_{00} + + {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.0 3.0} + + {μ μ}_{c c} {\overset{~ ~}{P P}}_{44} \\ s the s {\overset{~ ~}{P P}}_{11} = = {λ λ}_{0101} {\overset{~ ~}{P P}}_{00} - - (({λ λ}_{1212} + + {\overset{~ ~}{λ λ}}_{1313})) {\overset{~ ~}{P P}}_{11} + + {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.1 3.1} \\ s the s {\overset{~ ~}{P P}}_{22} = = {λ λ}_{1212} {\overset{~ ~}{P P}}_{11} - - (({λ λ}_{23 twenty three} + + {\overset{~ ~}{λ λ}}_{24 twenty four})) {\overset{~ ~}{P P}}_{22} + + {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.2 3.2} \\ s the s {\overset{~ ~}{P P}}_{3.2 3.2} = = {\overset{~ ~}{λ λ}}_{23 twenty three} {\overset{~ ~}{P P}}_{22} - - {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.2 3.2} \\ s the s {\overset{~ ~}{P P}}_{3.1 3.1} = = {\overset{~ ~}{λ λ}}_{1313} {\overset{~ ~}{P P}}_{11} - - {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.1 3.1} \\ s the s {\overset{~ ~}{P P}}_{3.0 3.0} = = {\overset{~ ~}{λ λ}}_{0303} {\overset{~ ~}{P P}}_{00} - - {μ μ}_{b b} {\overset{~ ~}{P P}}_{3.0 3.0} \\ s the s {\overset{~ ~}{P P}}_{44} = = {\overset{~ ~}{λ λ}}_{24 twenty four} {\overset{~ ~}{P P}}_{22} - - {μ μ}_{c c} {\overset{~ ~}{P P}}_{44} \end{matrix}

Among them, s is the complex frequency in the Laplace transform, and the Laplace transform is an integral transformation process that transforms a function in the time domain into a complex variable function in the complex frequency domain;

(4-2) With the Laplace transform complex frequency s as the independent variable, the probability of the transformer being in normal, attention and abnormal states and as the dependent variable, will and The relation to s is expressed in the standard form as follows:

{\overset{~ ~}{P P}}_{00} ((s the s)) = = {Σ Σ}_{i i = = 00}^{66} \frac{{\overset{~ ~}{L L}}_{00 i i}}{s the s - - {\overset{~ ~}{s the s}}_{i i}}

{\overset{~ ~}{P P}}_{11} ((s the s)) = = {Σ Σ}_{i i = = 00}^{88} \frac{{\overset{~ ~}{L L}}_{11 i i}}{s the s - - {\overset{~ ~}{s the s}}_{i i}}

{\overset{~ ~}{P P}}_{22} ((s the s)) = = {Σ Σ}_{i i = = 00}^{1010} \frac{{\overset{~ ~}{L L}}_{22 i i}}{s the s - - {\overset{~ ~}{s the s}}_{i i}}

in and is the intermediate coefficient in the standard form, usually a complex number, and its modulus usually ranges from 0 to 1;

(4-3) The above standard form is inversely transformed by Laplace, and the time-domain analytical expression of the probability that the transformer is in the normal, attention and abnormal states at time t is obtained as follows:

{\overset{~ ~}{P P}}_{00} = = {Σ Σ}_{i i = = 00}^{66} {\overset{~ ~}{L L}}_{00 i i} {e e}^{{\overset{~ ~}{s the s}}_{i i} t t}

{\overset{~ ~}{P P}}_{11} = = {Σ Σ}_{i i = = 00}^{88} {\overset{~ ~}{L L}}_{11 i i} {e e}^{{\overset{~ ~}{s the s}}_{i i} t t}

{\overset{~ ~}{P P}}_{22} = = {Σ Σ}_{i i = = 00}^{1010} {\overset{~ ~}{L L}}_{22 i i} {e e}^{{\overset{~ ~}{s the s}}_{i i} t t}

(4-4) According to the time-domain analytical expression of step (4-3), the availability of the transformer at time t is obtained The analytical formula is as follows:

\overset{~ ~}{A A} ((t t)) = = {\overset{~ ~}{P P}}_{00} + + {\overset{~ ~}{P P}}_{11} + + {\overset{~ ~}{P P}}_{22} = = {Σ Σ}_{i i = = 00}^{66} {\overset{~ ~}{L L}}_{00 i i} {e e}^{{\overset{~ ~}{s the s}}_{i i} t t} + + {Σ Σ}_{i i = = 00}^{88} {\overset{~ ~}{L L}}_{11 i i} {e e}^{{\overset{~ ~}{s the s}}_{i i} t t} + + {Σ Σ}_{i i = = 00}^{1010} {\overset{~ ~}{L L}}_{22 i i} {e e}^{{\overset{~ ~}{s the s}}_{i i} t t};;

(5) The availability of the above transformer at time t Expressed as a triangular fuzzy number, the form is as follows:

\overset{~ ~}{A A} ((t t)) = = ((\underset{&OverBar; &OverBar;}{A A} ((t t)),, \overset{^^}{A A} ((t t)),, \overset{&OverBar; &OverBar;}{A A} ((t t))))

where A (t) represents the lower limit of transformer availability at time t, Indicates the upper limit of the availability of the transformer at time t, Indicates the intermediate value of transformer availability at time t, and the solution process of the lower limit, upper limit and intermediate value is as follows:

(5-1) The upper limit of the sudden failure rate of the transformer using the above step (2) and Substituting step (3) for the burst failure rate in the Markovian state transition differential equations and The upper limit of the aging failure rate of the transformer using step (2) Instead of step (3) aging failure rate in Markov state transition differential equations Execute steps (4-1) to (4-4) to obtain the lower limit value A (t) of the availability of the transformer at time t;

(5-2) Use the lower limit values λ ₀₃ , λ ₁₃ and λ ₂₃ of the transformer sudden failure rate in the above step (2) to replace the sudden failure rate in the step (3) Markov state transition differential equations and Replace the aging failure rate in step (3) Markov state transition differential equations with the lower limit value λ of the transformer aging failure rate of step ( ₂ ) Execute steps (4-1) to (4-4) to obtain the upper limit of transformer availability at time t

(5-3) The median value of the sudden failure rate of the transformer using the above step (2) and Substituting step (3) for the burst failure rate in the Markovian state transition differential equations and The median value of transformer aging failure rate using step (2) Instead of step (3) aging failure rate in Markov state transition differential equations Execute steps (4-1) to (4-4) to obtain the intermediate value of transformer availability at time t

(6) Suppose the probability that the power grid is in a running state at time t for:

\overset{~ ~}{P P} ((t t)) = = \underset{i i &Element; &Element; {S S}_{o o n no}}{Π Π} {\overset{~ ~}{A A}}_{i i} ((t t)) \underset{i i &Element; &Element; {S S}_{o o f f f f}}{Π Π} ((11 - - {\overset{~ ~}{A A}}_{i i} ((t t))))

Among them, S _on represents the set of transformers in the working state of the power grid in this operating state, S _off represents the set of transformers in the fault state of the power grid in this operating state, and the subscript i represents the transformer number, Indicates the availability of the i-th transformer at time t;

(7) Assuming that the time length for the operation risk assessment of the power grid transformer is T, there are N transformers in the power grid, and the operation risk index of the power grid transformer is calculated The process is as follows:

(7-1) During initialization, set time t=0;

(7-2) Let t=t+1, the power grid transformer operation risk index at time t It is expressed as a triangular fuzzy number as follows:

\overset{&OverBar; &OverBar;}{R R} ((t t)) = = ((\underset{&OverBar; &OverBar;}{R R} ((t t)),, \overset{^^}{R R} ((t t)),, \overset{&OverBar; &OverBar;}{R R} ((t t))))

Where R (t) represents the lower limit value of the transformer operation risk index of the power grid at time t, Indicates the upper limit value of the transformer operation risk index of the power grid at time t, Indicates the median value of the transformer operation risk index of the power grid at time t, and the upper limit, lower limit and middle value of the transformer operation risk index of the power grid at time t are calculated as follows:

(7-2-1) Enumerate all operating states of the power grid at time t, and determine respectively the set of transformers S _on in the working state and the set of transformers S _off in the fault state under each operating state according to the operating state of the power grid;

(7-2-2) Using the grid power flow calculation method, calculate the load loss S _j (t) of the grid in each operating state, and the subscript j is the number of the operating state;

(7-2-3) For each operating state of the power grid, use the upper limit of the availability of each transformer in step (5) Instead of transformer availability in step (6) Utilize the formula of step (6) to calculate, and the calculation result is recorded as Use the following formula to calculate the lower limit value of the grid transformer operation risk index at time t:

\underset{&OverBar; &OverBar;}{R R} ((t t)) = = {Σ Σ}_{j j = = 11}^{22^{N N}} {\overset{&OverBar; &OverBar;}{P P}}_{j j} ((t t)) \cdot &Center Dot; {S S}_{j j} ((t t));;

(7-2-4) For each operating state of the power grid, replace the transformer availability in step (6) with the lower limit value A (t) of each transformer availability in step (5) Use the formula in step (6) to calculate, record the calculation result as P _j (t), and use the following formula to calculate the upper limit value of the grid transformer operation risk index at time t:

\overset{&OverBar; &OverBar;}{R R} ((t t)) = = {Σ Σ}_{j j = = 11}^{22^{N N}} {\underset{&OverBar; &OverBar;}{P P}}_{j j} ((t t)) \cdot \cdot {S S}_{j j} ((t t));;

(7-2-5) For each operating state of the power grid, use the median value of the availability of each transformer in step (5) Instead of transformer availability in step (6) Utilize the formula of step (6) to calculate, and the calculation result is recorded as Use the following formula to calculate the median value of the grid transformer operation risk index at time t:

\overset{^^}{R R} ((t t)) = = {Σ Σ}_{j j = = 11}^{22^{N N}} {\overset{^^}{P P}}_{j j} ((t t)) \cdot \cdot {S S}_{j j} ((t t));;

(7-3) judge the time t, if t<T, then return to step (7-2), if t=T, then use the above step (7-2) As a power grid transformer operation risk indicator.