CN106355284A - Optimal selection method of outgoing line of wind power plant - Google Patents

Abstract

Translated fromChinese

本发明公开了一种风电场送出线优化选型方法，包括以下步骤：S1：分别构建电力电缆热路模型和风力发电环境因素随机模型；S2：构建电力电缆线芯温度线性化模型，计算每个随机变量的各阶半不变量；S3：根据半不变量的性质和定义，求得电缆线芯温度的各阶半不变量；S4：运用Gram‑Charlier级数展开结合电缆线芯温度各阶半不变量获得状态变量线芯温度的概率密度函数和越限概率，从而进行优化选型。本发明方法考虑实际环境因素实时变化情况，将概率统计半不变量法引入到电力电缆选型中，获得能满足风电场可靠性的最优电缆选型，摈弃之前实际工程中安全裕度过高的电缆，显著减小风电场建设和后期运营管理费用。

The invention discloses a method for optimizing the type selection of the delivery line of a wind farm, which includes the following steps: S1: respectively constructing a power cable thermal circuit model and a random model of wind power generation environmental factors; S2: constructing a power cable core temperature linearization model, and calculating each The semi-invariants of each order of a random variable; S3: According to the nature and definition of the semi-invariants, obtain the semi-invariants of each order of the cable core temperature; S4: use the Gram-Charlier series expansion combined with each order of the cable core temperature The semi-invariant obtains the probability density function of the state variable wire core temperature and the probability of exceeding the limit, so as to optimize the selection. The method of the present invention considers the real-time changes of actual environmental factors, introduces the semi-invariant method of probability and statistics into the power cable selection, obtains the optimal cable selection that can meet the reliability of the wind farm, and discards the excessively high safety margin in the previous actual engineering Cables can significantly reduce the cost of wind farm construction and post-operation management.

Description

Translated fromChinese

一种风电场送出线优化选型方法A method for optimal selection of wind farm delivery lines

技术领域technical field

本发明涉及电力电缆工程设计领域，特别是设计一种风电场送出线优化选型方法。The invention relates to the field of power cable engineering design, in particular to a method for optimizing the type selection of a wind farm sending line.

背景技术Background technique

20世纪90年代以来，我国不断推动利用可再生能源政策，风电产业也得以迅速发展。“十三五”风电发展规划的提出，表明国家将加快风电发展步伐，其发展空间巨大。Since the 1990s, my country has continuously promoted the use of renewable energy policies, and the wind power industry has also developed rapidly. The proposal of the "Thirteenth Five-Year Plan" for wind power development shows that the country will accelerate the pace of wind power development, and its development space is huge.

风电场投资费用都较高，电气系统贯穿风力发电始终，在发电成本中占有很大比重。送出线作为电气系统主体部分，有必要提出一种既可靠又经济的送出线选型方法。在输电领域中，电缆是依据载流量进行选型判断的。实际风电场送出线往往依据100％恒定负载率和标准中特定环境条件下计算出的载流量进行选型，此方法选择出的电缆型号欠妥，特别是针对于风电场这样的变负载情况而言，浪费电缆线路载流能力，增加风电场建设及后期运营管理的时间和费用。The investment costs of wind farms are relatively high, and the electrical system runs through the wind power generation process, accounting for a large proportion of the cost of power generation. As the outgoing line is the main part of the electrical system, it is necessary to propose a reliable and economical selection method for the outgoing line. In the field of power transmission, cables are selected and judged according to their carrying capacity. The actual wind farm send-out line is often selected according to the 100% constant load rate and the current carrying capacity calculated under the specific environmental conditions in the standard. The cable type selected by this method is not suitable, especially for the variable load situation of the wind farm. In other words, the current-carrying capacity of the cable line is wasted, and the time and cost of wind farm construction and post-operation management are increased.

研究表明电缆载流量与其线芯温度有关，因此根据线芯温度确定其载流量对于提高电缆输电能力很有意义。对于风电场，影响电缆线芯温度的主导环境因素为风速和环境温度。目前，国内外研究学者用了很多不同的方法对电缆温度场进行了研究，根据电缆的传热特性，建立其热路模型。该模型能够依据固定负荷及环境因素参数计算线芯温度，但是鲜有文章考虑环境因素不确定性对风电场送出线进行规划，没有考虑环境参数实时变化情况对线芯温度的影响。然而，风力发电出力具有随机性和间歇性的特点，所以有必要研究随机变化因素对电缆运行状况的影响。Studies have shown that the ampacity of the cable is related to its core temperature, so determining the ampacity according to the core temperature is very meaningful for improving the power transmission capacity of the cable. For wind farms, the dominant environmental factors affecting cable core temperature are wind speed and ambient temperature. At present, researchers at home and abroad have used many different methods to study the cable temperature field, and established its thermal circuit model according to the heat transfer characteristics of the cable. This model can calculate the wire core temperature based on fixed load and environmental factor parameters, but few articles consider the uncertainty of environmental factors to plan the wind farm sending line, and do not consider the influence of real-time changes in environmental parameters on the core temperature. However, the output of wind power generation is random and intermittent, so it is necessary to study the influence of random variation factors on the operation of cables.

当前尚未有通过结合概率统计半不变量法考虑环境因素不确定性规划风电场送出线。At present, there is no planning of wind farm transmission lines by combining the semi-invariant method of probability and statistics to consider the uncertainty of environmental factors.

发明内容Contents of the invention

发明目的：本发明的目的是提供一种能够解决现有技术中存在的缺陷的风电场送出线优化选型方法。Purpose of the invention: The purpose of the present invention is to provide a method for optimizing the selection of wind farm transmission lines that can solve the defects in the prior art.

技术方案：为达到此目的，本发明采用以下技术方案：Technical scheme: in order to achieve this goal, the present invention adopts following technical scheme:

本发明所述的风电场送出线优化选型方法，包括以下步骤：The wind farm delivery line optimization selection method of the present invention comprises the following steps:

S1：分别构建电力电缆热路模型和风力发电环境因素随机模型；S1: Construct the thermal circuit model of power cables and the stochastic model of environmental factors of wind power generation respectively;

S2：构建电力电缆线芯温度线性化模型，计算每个随机变量的各阶半不变量；S2: Construct the linearization model of the core temperature of the power cable, and calculate the semi-invariant variables of each order for each random variable;

S3：根据半不变量的性质和定义，求得电缆线芯温度的各阶半不变量；S3: According to the nature and definition of the semi-invariant, obtain the semi-invariant of each order of the cable core temperature;

S4：运用Gram-Charlier级数展开结合电缆线芯温度各阶半不变量获得状态变量线芯温度的概率密度函数和越限概率，从而进行优化选型。S4: Use the Gram-Charlier series expansion combined with the semi-invariant variables of each order of the cable core temperature to obtain the probability density function of the state variable core temperature and the probability of exceeding the limit, so as to optimize the selection.

进一步，所述步骤S1包括以下步骤：Further, the step S1 includes the following steps:

S1.1：构建电力电缆热路模型；S1.1: Construct the power cable thermal circuit model;

S1.2：建立风速随机模型；S1.2: Establish a random wind speed model;

运用Weibull分布函数描述风速，风速的概率密度数学模型如式(1)所示：Using the Weibull distribution function to describe the wind speed, the mathematical model of the probability density of the wind speed is shown in formula (1):

$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>v</span>v</span>}}_{\mathrm{<span><span>w</span>w</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>c</span>c</span>}}{<span><span>(</span>(</span>\frac{{\mathrm{<span><span>v</span>v</span>}}_{\mathrm{<span><span>w</span>w</span>}}}{\mathrm{<span><span>c</span>c</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>e</span>e</span>}}^{<span><span>\&lsqb;</span>\&lsqb;</span><span><span>-</span>-</span>{<span><span>(</span>(</span>\frac{{\mathrm{<span><span>v</span>v</span>}}_{\mathrm{<span><span>w</span>w</span>}}}{\mathrm{<span><span>c</span>c</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>k</span>k</span>}}<span><span>\&rsqb;</span>\&rsqb;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>$

式(1)中，c为标度参数，k为形状参数，v_w为风速(m/s)；In formula (1), c is the scale parameter, k is the shape parameter, v_w is the wind speed (m/s);

通过风电机的输出功率与风速间的近似一次线性关系得到风电机出力的随机分布，其概率密度数学模型如式(2)所示：The random distribution of wind turbine output is obtained through the approximate linear relationship between the output power of the wind turbine and the wind speed, and its probability density mathematical model is shown in formula (2):

$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>w</span>w</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>A</span>A</span>}\mathrm{<span><span>c</span>c</span>}}{<span><span>(</span>(</span>\frac{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>w</span>w</span>}}<span><span>+</span>+</span>\mathrm{<span><span>B</span>B</span>}}{\mathrm{<span><span>A</span>A</span>}\mathrm{<span><span>c</span>c</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>e</span>e</span>}}^{<span><span>\&lsqb;</span>\&lsqb;</span><span><span>-</span>-</span>{<span><span>(</span>(</span>\frac{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>w</span>w</span>}}<span><span>+</span>+</span>\mathrm{<span><span>B</span>B</span>}}{\mathrm{<span><span>A</span>A</span>}\mathrm{<span><span>c</span>c</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>k</span>k</span>}}<span><span>\&rsqb;</span>\&rsqb;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>2</span>2</span>}<span><span>)</span>)</span>$

式(2)中，P_w为风电机输出功率，A＝P_r/(v_r-v_ci)，B＝P_rv_ci/(v_r-v_ci)，P_r为风电机额定功率，v_r为风电机额定风速，v_ci为风电机切入风速；In formula (2), P_w is the output power of the wind generator, A=P_r /(v_r -v_ci ), B=P_r v_ci /(v_r -v_ci ), P_r is the rated power of the wind motor, v_r is the rated wind speed of the wind turbine, and v_ci is the cut-in wind speed of the wind turbine;

由Weibull分布的定理推得电缆电流概率密度函数为：According to the theorem of Weibull distribution, the probability density function of cable current is deduced as:

$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>\mathrm{<span><span>I</span>I</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\mathrm{<span><span>D</span>D.</span>}\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>A</span>A</span>}\mathrm{<span><span>c</span>c</span>}}{<span><span>(</span>(</span>\frac{<span><span>(</span>(</span>\mathrm{<span><span>I</span>I</span>}<span><span>+</span>+</span>\mathrm{<span><span>B</span>B</span>}<span><span>)</span>)</span>\mathrm{<span><span>D</span>D.</span>}}{\mathrm{<span><span>A</span>A</span>}\mathrm{<span><span>c</span>c</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>e</span>e</span>}}^{<span><span>\&lsqb;</span>\&lsqb;</span><span><span>-</span>-</span>{<span><span>(</span>(</span>\frac{<span><span>(</span>(</span>\mathrm{<span><span>I</span>I</span>}<span><span>+</span>+</span>\mathrm{<span><span>B</span>B</span>}<span><span>)</span>)</span>\mathrm{<span><span>D</span>D.</span>}}{\mathrm{<span><span>A</span>A</span>}\mathrm{<span><span>c</span>c</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>k</span>k</span>}}<span><span>\&rsqb;</span>\&rsqb;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>3</span>3</span>}<span><span>)</span>)</span>$

式(3)中，U为电缆电压等级，cosθ为额定功率因数，n为风机个数，I为电缆电流；In formula (3), U is the cable voltage level, cosθ is the rated power factor, n is the number of fans, and I is the cable current;

S1.3：建立环境温度随机模型；S1.3: Establish a random model of ambient temperature;

环境温度采样数据运用正态分布，其概率密度函数为：The ambient temperature sampling data uses a normal distribution, and its probability density function is:

$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>a</span>a</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\sqrt{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}}\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}{\mathrm{<span><span>e</span>e</span>}}^{<span><span>\&lsqb;</span>\&lsqb;</span>\frac{{<span><span>(</span>(</span>{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>a</span>a</span>}}<span><span>-</span>-</span>\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>2</span>2</span>}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\&rsqb;</span>\&rsqb;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$

式(4)中，θ_a为环境温度采样数据，μ为均值，σ²为方差；In formula (4), θ_a is the ambient temperature sampling data, μ is the mean value, and σ² is the variance;

S1.4：输入原始参数数据，选取组合最差工况进行研究。S1.4: Input the original parameter data and select the combined worst working conditions for research.

进一步，所述步骤S2包括以下步骤：Further, the step S2 includes the following steps:

S2.1：建立电力电缆线芯温度线性化模型；S2.1: Establish a linearization model of the power cable core temperature;

电缆电流数学模型为：The mathematical model of cable current is:

I²{R[T₁+(1+λ₁)T₂+(1+λ₁+λ₂)(T₃+T₄)]}＝θ_c-θ_a-W_d[0.5T₁+T₂+T₃+T₄] (5)式(5)中，I为电缆电流，R为电缆交流电阻，T₁为绝缘层热阻，T₂为金属屏蔽层热阻，T₃为铠装层外部护套热阻，T₄为电缆敷设环境土壤的热阻，λ₁为电缆金属层损耗系数，λ₂为铠装损耗系数，θ_c为线芯工作温度，W_d为单位长度绝缘介质的损耗，U₀为电缆导体对地电压，w＝2πf，其中f为电源频率，C为单位长度电缆的电容，tanδ为绝缘介质的损耗角正切；I² {R[T₁ +(1+λ₁ )T₂ +(1+λ₁ +λ₂ )(T₃ +T₄ )]}＝θ_c -θ_a -W_d [0.5T₁ +T₂ +T₃ +T₄ ] (5) In formula (5), I is the cable current, R is the AC resistance of the cable, T₁ is the thermal resistance of the insulation layer, T₂ is the thermal resistance of the metal shielding layer, and T₃ is the armored layer outer sheath thermal resistance, T₄ is the thermal resistance of the cable laying environment soil, λ₁ is the loss coefficient of the cable metal layer, λ₂ is the armor loss coefficient, θ_c is the working temperature of the wire core, W_d is the insulation medium per unit length loss of U₀ is the voltage of the cable conductor to the ground, w=2πf, where f is the power frequency, C is the capacitance of the cable per unit length, and tanδ is the loss tangent of the insulating medium;

并且式(5)满足：And formula (5) satisfies:

Δθ_c＝2AI₀ΔI+Δθ_a (6)Δθ_c ＝2AI₀ ΔI+Δθ_a (6)

式(6)中，Δθ_c为电缆线芯工作温度与其期望值的差值，I₀为电缆电流期望值，ΔI为电缆电流与其期望值的差值，Δθ_a为环境温度与其期望值的差值；In formula (6), Δθ_c is the difference between the working temperature of the cable core and its expected value, I₀ is the expected value of the cable current, ΔI is the difference between the cable current and its expected value, and Δθ_a is the difference between the ambient temperature and its expected value;

S2.2：根据式(3)和式(4)将电缆电流和环境温度离散化，然后由随机变量分布函数求得各离散值的概率，并根据式(7)计算电流和环境温度随机变量的各阶矩，再根据式(8)计算各阶半不变量；S2.2: According to formula (3) and formula (4), the cable current and ambient temperature are discretized, and then the probability of each discrete value is obtained by the random variable distribution function, and the current and ambient temperature random variables are calculated according to formula (7) Moments of each order, and then calculate semi-invariants of each order according to formula (8);

${\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>r</span>r</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}{\mathrm{<span><span>p</span>p</span>}}_{\mathrm{<span><span>i</span>i</span>}}{<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>-</span>-</span>\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>)</span>)</span>}^{\mathrm{<span><span>r</span>r</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>7</span>7</span>}<span><span>)</span>)</span>$

式(7)中，M_r为电流及环境温度的各阶矩，1≤r≤8，p_i为电流及环境温度的概率值，x_i为电流及环境温度的离散值，μ为电流及环境温度的期望值，1≤i≤电流及环境温度离散值的个数；In formula (7), M_r is the moment of each order of current and ambient temperature, 1≤r≤8, p_i is the probability value of current and ambient temperature, x_i is the discrete value of current and ambient temperature, μ is the current and The expected value of ambient temperature, 1≤i≤the number of discrete values of current and ambient temperature;

$\begin{array}{c}\begin{array}{ccc}{\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>=</span>=</span>\mathrm{<span><span>\&mu;</span>\&mu;</span>}& {\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}& {\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>3</span>3</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>3</span>3</span>}}\end{array}\\ {\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>4</span>4</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>4</span>4</span>}}<span><span>-</span>-</span>\mathrm{<span><span>3</span>3</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}^{\mathrm{<span><span>2</span>2</span>}}\\ {\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>5</span>5</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>5</span>5</span>}}<span><span>-</span>-</span>\mathrm{<span><span>10</span>10</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>3</span>3</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}\\ {\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>6</span>6</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>6</span>6</span>}}<span><span>-</span>-</span>\mathrm{<span><span>15</span>15</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>4</span>4</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span>\mathrm{<span><span>10</span>10</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>3</span>3</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>\mathrm{<span><span>30</span>30</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}^{\mathrm{<span><span>3</span>3</span>}}\\ {\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>7</span>7</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>7</span>7</span>}}<span><span>-</span>-</span>\mathrm{<span><span>21</span>twenty\; one</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>5</span>5</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span>\mathrm{<span><span>35</span>35</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>4</span>4</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>3</span>3</span>}}<span><span>+</span>+</span>\mathrm{<span><span>210</span>210</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>3</span>3</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}^{\mathrm{<span><span>2</span>2</span>}}\\ {\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>8</span>8</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>8</span>8</span>}}<span><span>-</span>-</span>\mathrm{<span><span>28</span>28</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>6</span>6</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span>\mathrm{<span><span>56</span>56</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>5</span>5</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>3</span>3</span>}}<span><span>-</span>-</span>\mathrm{<span><span>35</span>35</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>4</span>4</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>\mathrm{<span><span>420</span>420</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>4</span>4</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>\mathrm{<span><span>560</span>560</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>3</span>3</span>}}^{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span>\mathrm{<span><span>630</span>630</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}^{\mathrm{<span><span>4</span>4</span>}}\end{array}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$

式(8)中，N_r为电流及环境温度的各阶半不变量。In formula (8), N_r is each order semi-invariant of current and ambient temperature.

进一步，所述步骤S4中的状态变量线芯温度的概率密度函数f(x)为：Further, the probability density function f(x) of the state variable wire core temperature in the step S4 is:

$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>\&psi;</span>\&psi;</span>}<span><span>(</span>(</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>x</span>x</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>\mathrm{<span><span>\&psi;</span>\&psi;</span>}<span><span>(</span>(</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>x</span>x</span>}}<span><span>)</span>)</span><span><span>\&lsqb;</span>\&lsqb;</span>\frac{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>3</span>3</span>}}}{\mathrm{<span><span>3</span>3</span>}<span><span>!</span>!</span>}{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>3</span>3</span>}}<span><span>(</span>(</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>x</span>x</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>\frac{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>4</span>4</span>}}}{\mathrm{<span><span>4</span>4</span>}<span><span>!</span>!</span>}{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>4</span>4</span>}}<span><span>(</span>(</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>x</span>x</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>\frac{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}}{\mathrm{<span><span>5</span>5</span>}<span><span>!</span>!</span>}{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>5</span>5</span>}}<span><span>(</span>(</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>x</span>x</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>\frac{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>6</span>6</span>}}<span><span>+</span>+</span>\mathrm{<span><span>10</span>10</span>}{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>3</span>3</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>6</span>6</span>}<span><span>!</span>!</span>}{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>6</span>6</span>}}<span><span>(</span>(</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>x</span>x</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>\frac{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>7</span>7</span>}}<span><span>+</span>+</span>\mathrm{<span><span>35</span>35</span>}{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>3</span>3</span>}}{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>4</span>4</span>}}}{\mathrm{<span><span>7</span>7</span>}<span><span>!</span>!</span>}{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>7</span>7</span>}}<span><span>(</span>(</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>x</span>x</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>\frac{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>8</span>8</span>}}<span><span>+</span>+</span>\mathrm{<span><span>56</span>56</span>}{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>3</span>3</span>}}{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>5</span>5</span>}}<span><span>+</span>+</span>\mathrm{<span><span>35</span>35</span>}{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>4</span>4</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>8</span>8</span>}<span><span>!</span>!</span>}{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>8</span>8</span>}}<span><span>(</span>(</span>\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>x</span>x</span>}}<span><span>)</span>)</span><span><span>+</span>+</span><span><span>...</span>...</span><span><span>\&rsqb;</span>\&rsqb;</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>9</span>9</span>}<span><span>)</span>)</span>$

式(9)中，为状态变量线芯温度的标准正态密度函数；为规格化后的状态变量线芯温度，即μ为状态变量线芯温度的期望，σ²为状态变量线芯温度的方差，g_r为规格化后的电缆线芯温度各阶半不变量，即N_r为电缆线芯温度的r阶半不变量，1≤r≤8，为Hermite多项式。In formula (9), is the standard normal density function of the state variable core temperature; is the normalized state variable wire core temperature, namely μ is the expectation of the core temperature of the state variable,^σ2 is the variance of the core temperature of the state variable, and g_r is the semi-invariant variable of each order of the normalized cable core temperature, namely N_r is the r-order semi-invariant of cable core temperature, 1≤r≤8, is a Hermite polynomial.

有益效果：本发明方法考虑实际环境因素实时变化情况，将概率统计半不变量法引入到电力电缆选型中，获得能满足风电场可靠性的最优电缆选型，摈弃之前实际工程中安全裕度过高的电缆，显著减小风电场建设和后期运营管理费用。Beneficial effects: the method of the present invention considers the real-time changes of actual environmental factors, introduces the semi-invariant method of probability and statistics into the selection of power cables, obtains the optimal selection of cables that can meet the reliability of wind farms, and discards the safety margins in previous actual projects. Excessively high cables can significantly reduce the construction and post-operation management costs of wind farms.

附图说明Description of drawings

图1为本发明的电力电缆热路模型的示意图；Fig. 1 is the schematic diagram of electric cable thermal circuit model of the present invention;

图2为本发明具体实施方式中YJQ41G-500型海缆线芯温度概率分布曲线；Fig. 2 is the YJQ41G-500 type submarine cable core temperature probability distribution curve in the specific embodiment of the present invention;

图3为本发明具体实施方式中YJQ41G-400型海缆线芯温度概率分布曲线；Fig. 3 is the YJQ41G-400 type submarine cable core temperature probability distribution curve in the specific embodiment of the present invention;

图4为本发明的具体实施方式中YJQ41G-400型海缆线芯温度概率密度函数曲线；Fig. 4 is YJQ41G-400 type submarine cable core temperature probability density function curve in the specific embodiment of the present invention;

图5为本发明的方法流程图。Fig. 5 is a flow chart of the method of the present invention.

具体实施方式detailed description

下面结合具体实施方式对本发明的技术方案作进一步的介绍。The technical solution of the present invention will be further introduced below in combination with specific embodiments.

本发明公开了一种风电场送出线优化选型方法，如图5所示，包括以下步骤：The invention discloses a method for optimizing the type selection of a wind farm delivery line, as shown in Figure 5, comprising the following steps:

S1：分别构建电力电缆热路模型和风力发电环境因素随机模型；S1: Construct the thermal circuit model of power cables and the stochastic model of environmental factors of wind power generation respectively;

S2：构建电力电缆线芯温度线性化模型，计算每个随机变量的各阶半不变量；S2: Construct the linearization model of the core temperature of the power cable, and calculate the semi-invariant variables of each order for each random variable;

S3：根据半不变量的性质和定义，求得电缆线芯温度的各阶半不变量；S3: According to the nature and definition of the semi-invariant, obtain the semi-invariant of each order of the cable core temperature;

S4：运用Gram-Charlier级数展开结合电缆线芯温度各阶半不变量获得状态变量线芯温度的概率密度函数和越限概率，从而进行优化选型。S4: Use the Gram-Charlier series expansion combined with the semi-invariant variables of each order of the cable core temperature to obtain the probability density function of the state variable core temperature and the probability of exceeding the limit, so as to optimize the selection.

下面介绍一个采用了本发明方法的海上风电场的实施例：Introduce an embodiment of the offshore wind farm that has adopted the method of the present invention below:

选取容量为150MW的江苏某海上风电场，该风电场安装60台风机，型号为GW100/2500，额定风速为12.5m/s，切入、切出风速分别为3m/s和25m/s。综合考虑相关不确定性环境因素，对其110kV送出线进行优化选型。An offshore wind farm in Jiangsu with a capacity of 150MW is selected. The wind farm is equipped with 60 wind turbines, the model is GW100/2500, the rated wind speed is 12.5m/s, and the cut-in and cut-out wind speeds are 3m/s and 25m/s respectively. Considering the relevant uncertain environmental factors comprehensively, the optimal selection of its 110kV transmission line is carried out.

S1：构建海底电缆热路模型，如图1所示；构建海上风力发电环境因素随机模型，具体包括风速随机模型和环境温度随机模型；S1: Build a submarine cable heat path model, as shown in Figure 1; build a random model of environmental factors for offshore wind power generation, specifically including a random model of wind speed and a random model of ambient temperature;

S1.1：构建电力电缆热路模型；S1.1: Construct the power cable thermal circuit model;

风电场电缆长度远大于其埋设深度，将其温度场分布简化成二维场问题求解，运用电缆载流量热-电类比法，将电缆细分到每层。各层热源比作电流源；各层热阻比作电阻；各层热容比作电容，如图1所示。电缆内的热量经过绝缘和外层金属铠装的热阻，散发至周围土壤。The length of the cable in the wind farm is much longer than its burial depth, so the temperature field distribution is simplified into a two-dimensional field problem, and the cable is subdivided into each layer by using the thermal-electrical analogy method of cable ampacity. The heat source of each layer is compared to a current source; the thermal resistance of each layer is compared to a resistance; the heat capacity of each layer is compared to a capacitor, as shown in Figure 1. The heat in the cable is dissipated to the surrounding soil through the thermal resistance of the insulation and the outer metal armor.

每层的温升等于流过这层的热流乘以该层的热阻，于是，电缆电流的数学模型为：The temperature rise of each layer is equal to the heat flow through this layer multiplied by the thermal resistance of the layer, so the mathematical model of the cable current is:

$\mathrm{<span><span>I</span>I</span>}<span><span>=</span>=</span>{<span><span>\&lsqb;</span>\&lsqb;</span>\frac{{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>c</span>c</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>a</span>a</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>W</span>W</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>\&lsqb;</span>\&lsqb;</span>\mathrm{<span><span>0.5</span>0.5</span>}{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>3</span>3</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>4</span>4</span>}}<span><span>\&rsqb;</span>\&rsqb;</span>}{\mathrm{<span><span>R</span>R</span>}<span><span>\&lsqb;</span>\&lsqb;</span>{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>+</span>+</span><span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span><span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span><span><span>(</span>(</span>{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>3</span>3</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>4</span>4</span>}}<span><span>)</span>)</span><span><span>\&rsqb;</span>\&rsqb;</span>}<span><span>\&rsqb;</span>\&rsqb;</span>}^{\mathrm{<span><span>0.5</span>0.5</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>$

式(1)中，I为电缆电流，R为电缆交流电阻，T₁为绝缘层热阻，T₂为金属屏蔽层热阻，T₃为铠装层外部护套热阻，T₄为电缆敷设环境土壤的热阻，λ₁为电缆金属层损耗系数，λ₂为铠装损耗系数，θ_c为线芯工作温度，θ_a为环境温度采样数据，W_d为单位长度绝缘介质的损耗，U₀为电缆导体对地电压，w＝2πf，其中f为电源频率，C为单位长度电缆的电容，tanδ为绝缘介质的损耗角正切；In formula (1), I is the cable current, R is the AC resistance of the cable, T₁ is the thermal resistance of the insulation layer, T₂ is the thermal resistance of the metal shielding layer, T₃ is the thermal resistance of the outer sheath of the armored layer, and T₄ is the thermal resistance of the cable The thermal resistance of the laying environment soil, λ₁ is the loss coefficient of the cable metal layer, λ₂ is the armor loss coefficient, θ_c is the working temperature of the wire core, θ_a is the sampling data of the ambient temperature, W_d is the loss of the insulating medium per unit length, U₀ is the voltage of the cable conductor to the ground, w=2πf, where f is the power frequency, C is the capacitance of the cable per unit length, and tanδ is the loss tangent of the insulating medium;

S1.2：建立风速随机模型；S1.2: Establish a random wind speed model;

运用Weibull分布函数描述风速，风速的概率密度数学模型如式(2)所示：Using the Weibull distribution function to describe the wind speed, the mathematical model of the probability density of the wind speed is shown in formula (2):

$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>v</span>v</span>}}_{\mathrm{<span><span>w</span>w</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>c</span>c</span>}}{<span><span>(</span>(</span>\frac{{\mathrm{<span><span>v</span>v</span>}}_{\mathrm{<span><span>w</span>w</span>}}}{\mathrm{<span><span>c</span>c</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>e</span>e</span>}}^{<span><span>\&lsqb;</span>\&lsqb;</span><span><span>-</span>-</span>{<span><span>(</span>(</span>\frac{{\mathrm{<span><span>v</span>v</span>}}_{\mathrm{<span><span>w</span>w</span>}}}{\mathrm{<span><span>c</span>c</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>k</span>k</span>}}<span><span>\&rsqb;</span>\&rsqb;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>2</span>2</span>}<span><span>)</span>)</span>$

式(2)中，c为标度参数，k为形状参数，v_w为风速(m/s)；In formula (2), c is the scale parameter, k is the shape parameter, and v_w is the wind speed (m/s);

通过风电机的输出功率与风速间的近似一次线性关系得到风电机出力的随机分布，其概率密度数学模型如式(3)所示：The random distribution of wind turbine output is obtained through the approximate linear relationship between the output power of the wind turbine and the wind speed, and its probability density mathematical model is shown in formula (3):

$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>w</span>w</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>A</span>A</span>}\mathrm{<span><span>c</span>c</span>}}{<span><span>(</span>(</span>\frac{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>w</span>w</span>}}<span><span>+</span>+</span>\mathrm{<span><span>B</span>B</span>}}{\mathrm{<span><span>A</span>A</span>}\mathrm{<span><span>c</span>c</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>e</span>e</span>}}^{<span><span>\&lsqb;</span>\&lsqb;</span><span><span>-</span>-</span>{<span><span>(</span>(</span>\frac{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>w</span>w</span>}}<span><span>+</span>+</span>\mathrm{<span><span>B</span>B</span>}}{\mathrm{<span><span>A</span>A</span>}\mathrm{<span><span>c</span>c</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>k</span>k</span>}}<span><span>\&rsqb;</span>\&rsqb;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>3</span>3</span>}<span><span>)</span>)</span>$

式(3)中，P_w为风电机输出功率，A＝P_r/(v_r-v_ci)，B＝P_rv_ci/(v_r-v_ci)，P_r为风电机额定功率，v_r为风电机额定风速，v_ci为风电机切入风速；In formula (3), P_w is the output power of the wind generator, A=P_r /(v_r -v_ci ), B=P_r v_ci /(v_r -v_ci ), P_r is the rated power of the wind generator, v_r is the rated wind speed of the wind turbine, and v_ci is the cut-in wind speed of the wind turbine;

由Weibull分布的定理推得电缆电流概率密度函数为：According to the theorem of Weibull distribution, the probability density function of cable current is deduced as:

$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>\mathrm{<span><span>I</span>I</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\mathrm{<span><span>D</span>D.</span>}\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>A</span>A</span>}\mathrm{<span><span>c</span>c</span>}}{<span><span>(</span>(</span>\frac{<span><span>(</span>(</span>\mathrm{<span><span>I</span>I</span>}<span><span>+</span>+</span>\mathrm{<span><span>B</span>B</span>}<span><span>)</span>)</span>\mathrm{<span><span>D</span>D.</span>}}{\mathrm{<span><span>A</span>A</span>}\mathrm{<span><span>c</span>c</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>e</span>e</span>}}^{<span><span>\&lsqb;</span>\&lsqb;</span><span><span>-</span>-</span>{<span><span>(</span>(</span>\frac{<span><span>(</span>(</span>\mathrm{<span><span>I</span>I</span>}<span><span>+</span>+</span>\mathrm{<span><span>B</span>B</span>}<span><span>)</span>)</span>\mathrm{<span><span>D</span>D.</span>}}{\mathrm{<span><span>A</span>A</span>}\mathrm{<span><span>c</span>c</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>k</span>k</span>}}<span><span>\&rsqb;</span>\&rsqb;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$

式(4)中，U为电缆电压等级，cosθ为额定功率因数，n为风机个数，I为电缆电流；In formula (4), U is the cable voltage level, cosθ is the rated power factor, n is the number of fans, and I is the cable current;

S1.3：建立环境温度随机模型；S1.3: Establish a random model of ambient temperature;

环境温度采样数据运用正态分布，其概率密度函数为：The ambient temperature sampling data uses a normal distribution, and its probability density function is:

$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>a</span>a</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\sqrt{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;</span>\&pi;</span>}}\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}{\mathrm{<span><span>e</span>e</span>}}^{<span><span>\&lsqb;</span>\&lsqb;</span><span><span>-</span>-</span>\frac{{<span><span>(</span>(</span>{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>a</span>a</span>}}<span><span>-</span>-</span>\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>2</span>2</span>}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\&rsqb;</span>\&rsqb;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>5</span>5</span>}<span><span>)</span>)</span>$

式(5)中，θ_a为环境温度采样数据，μ为均值，σ²为方差；In formula (5), θ_a is the ambient temperature sampling data, μ is the mean value, and σ² is the variance;

S1.4：输入原始参数数据，选取组合最差工况进行研究，即风速随机模型选取12月参数，如表1所示，环境温度随机参数选取夏季参数，如表2所示。S1.4: Input the original parameter data, and select the worst combined working conditions for research, that is, select the December parameters for the wind speed random model, as shown in Table 1, and select the summer parameters for the ambient temperature random parameters, as shown in Table 2.

表1 80m高处风速月威布尔参数Table 1 Monthly Weibull parameters of wind speed at 80m height

表2 夏季海底环境温度参数Table 2 Environmental temperature parameters of seabed in summer

S2：构建电力电缆线芯温度线性化模型，计算每个随机变量的各阶半不变量；S2: Construct the linearization model of the core temperature of the power cable, and calculate the semi-invariant variables of each order for each random variable;

S2.1：建立电力电缆线芯温度线性化模型；S2.1: Establish a linearization model of the power cable core temperature;

电缆电流数学模型为：The mathematical model of cable current is:

I²{R[T₁+(1+λ₁)T₂+(1+λ₁+λ₂)(T₃+T₄)]}＝θ_c-θ_a-W_d[0.5T₁+T₂+T₃+T₄] (6)I² {R[T₁ +(1+λ₁ )T₂ +(1+λ₁ +λ₂ )(T₃ +T₄ )]}＝θ_c -θ_a -W_d [0.5T₁ +T₂ +T₃ +T₄ ] (6)

式(6)中，R为电缆交流电阻，T₁为绝缘层热阻，T₂为金属屏蔽层热阻，T₃为铠装层外部护套热阻，T₄为电缆敷设环境土壤的热阻，λ₁为电缆金属层损耗系数，λ₂为铠装损耗系数，θ_c为线芯工作温度，W_d为单位长度绝缘介质的损耗，U₀为电缆导体对地电压，w＝2πf，其中f为电源频率，C为单位长度电缆的电容，tanδ为绝缘介质的损耗角正切；In formula (6), R is the AC resistance of the cable, T₁ is the thermal resistance of the insulating layer, T₂ is the thermal resistance of the metal shielding layer, T₃ is the thermal resistance of the outer sheath of the armored layer, and T₄ is the thermal resistance of the cable laying environment soil resistance, λ₁ is the loss coefficient of the cable metal layer, λ₂ is the armor loss coefficient, θ_c is the working temperature of the wire core, W_d is the loss of the insulation medium per unit length, U₀ is the voltage of the cable conductor to the ground, w=2πf, where f is the power frequency, C is the capacitance of the cable per unit length, and tanδ is the loss tangent of the insulating medium;

当海缆参数确定时，将各常量系数简化得：When the submarine cable parameters are determined, the constant coefficients are simplified to:

I²A＝θ_c-θ_a-Bθ_c＝I²A+θ_a+B (7)I² A = θ_c - θ_a - B θ_c = I² A + θ_a + B (7)

将此式进行泰勒级数展开得：The Taylor series expansion of this formula gives:

${\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>c</span>c</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&Delta;\&theta;</span>\&Delta;\&theta;</span>}}_{\mathrm{<span><span>c</span>c</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>I</span>I</span>}}_{\mathrm{<span><span>0</span>0</span>}}^{\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>A</span>A</span>}<span><span>+</span>+</span>\mathrm{<span><span>2</span>2</span>}{\mathrm{<span><span>AI</span>AI</span>}}_{\mathrm{<span><span>0</span>0</span>}}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}\mathrm{<span><span>I</span>I</span>}<span><span>+</span>+</span>{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>a</span>a</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&Delta;\&theta;</span>\&Delta;\&theta;</span>}}_{\mathrm{<span><span>a</span>a</span>}}<span><span>+</span>+</span>\mathrm{<span><span>B</span>B</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$

将下标带0的量设定为期望值，那么有：Set the amount with subscript 0 as the expected value, then:

${\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>c</span>c</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>I</span>I</span>}}_{\mathrm{<span><span>0</span>0</span>}}^{\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>A</span>A</span>}<span><span>+</span>+</span>{\mathrm{<span><span>\&theta;</span>\&theta;</span>}}_{\mathrm{<span><span>a</span>a</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>+</span>+</span>\mathrm{<span><span>B</span>B</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>9</span>9</span>}<span><span>)</span>)</span>$

所以：so:

Δθ_c＝2AI₀ΔI+Δθ_a (10)Δθ_c ＝2AI₀ ΔI+Δθ_a (10)

S2.2：根据式(4)和式(5)将电缆电流和环境温度离散化，然后由随机变量分布函数求得各离散值的概率，并根据式(11)计算电流和环境温度随机变量的各阶矩，再根据式(12)计算各阶半不变量；S2.2: According to the formula (4) and formula (5), the cable current and the ambient temperature are discretized, and then the probability of each discrete value is obtained by the distribution function of the random variable, and the random variable of the current and the ambient temperature is calculated according to the formula (11) Moments of each order, and then calculate semi-invariants of each order according to formula (12);

${\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>r</span>r</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}}{<span><span>\&Sigma;</span>\&Sigma;</span>}{\mathrm{<span><span>p</span>p</span>}}_{\mathrm{<span><span>i</span>i</span>}}{<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>-</span>-</span>\mathrm{<span><span>\&mu;</span>\&mu;</span>}<span><span>)</span>)</span>}^{\mathrm{<span><span>r</span>r</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>11</span>11</span>}<span><span>)</span>)</span>$

式(11)中，M_r为电流及环境温度的各阶矩，1≤r≤8，p_i为电流及环境温度的概率值，x_i为电流及环境温度的离散值，μ为电流及环境温度的期望值，1≤i≤电流及环境温度离散值的个数；In formula (11), M_r is the moment of each order of current and ambient temperature, 1≤r≤8, p_i is the probability value of current and ambient temperature, x_i is the discrete value of current and ambient temperature, μ is the current and The expected value of ambient temperature, 1≤i≤the number of discrete values of current and ambient temperature;

$\begin{array}{c}\begin{array}{ccc}{\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>=</span>=</span>\mathrm{<span><span>\&mu;</span>\&mu;</span>}& {\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}& {\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>3</span>3</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>3</span>3</span>}}\end{array}\\ {\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>4</span>4</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>4</span>4</span>}}<span><span>-</span>-</span>\mathrm{<span><span>3</span>3</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}^{\mathrm{<span><span>2</span>2</span>}}\\ {\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>5</span>5</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>5</span>5</span>}}<span><span>-</span>-</span>\mathrm{<span><span>10</span>10</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>3</span>3</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}\\ {\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>6</span>6</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>6</span>6</span>}}<span><span>-</span>-</span>\mathrm{<span><span>15</span>15</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>4</span>4</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span>\mathrm{<span><span>10</span>10</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>3</span>3</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>\mathrm{<span><span>30</span>30</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}^{\mathrm{<span><span>3</span>3</span>}}\\ {\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>7</span>7</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>7</span>7</span>}}<span><span>-</span>-</span>\mathrm{<span><span>21</span>twenty\; one</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>5</span>5</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span>\mathrm{<span><span>35</span>35</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>4</span>4</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>3</span>3</span>}}<span><span>+</span>+</span>\mathrm{<span><span>210</span>210</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>3</span>3</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}^{\mathrm{<span><span>2</span>2</span>}}\\ {\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>8</span>8</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>8</span>8</span>}}<span><span>-</span>-</span>\mathrm{<span><span>28</span>28</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>6</span>6</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span>\mathrm{<span><span>56</span>56</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>5</span>5</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>3</span>3</span>}}<span><span>-</span>-</span>\mathrm{<span><span>35</span>35</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>4</span>4</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>\mathrm{<span><span>420</span>420</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>4</span>4</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>\mathrm{<span><span>560</span>560</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>3</span>3</span>}}^{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span>\mathrm{<span><span>630</span>630</span>}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>2</span>2</span>}}^{\mathrm{<span><span>4</span>4</span>}}\end{array}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$

式(12)中，N_r为电流及环境温度的各阶半不变量。In formula (12), N_r is each order semi-invariant of current and ambient temperature.

表3给出了负载和环境温度前8阶半不变量的计算值。Table 3 gives the calculated values of the first 8 semi-invariants of load and ambient temperature.

表3 负载和温度各阶半不变量Table 3 The semi-invariants of each order of load and temperature

S3：本发明优化选型过程中，首先对150MW海上风电场常用型号YJQ41G-500进行计算分析。根据步骤S3以及半不变量的性质和定义，可得线芯温度各阶半不变量，计算结果如表4所示。S3: In the optimization selection process of the present invention, calculation and analysis of YJQ41G-500, which is commonly used in 150MW offshore wind farms, is performed first. According to step S3 and the properties and definitions of the semi-invariants, the semi-invariants of each order of core temperature can be obtained, and the calculation results are shown in Table 4.

S4：各阶半不变量由Gram-Charlier级数展开求得该型号海缆线芯温度分布函数，如图2所示。S4: The temperature distribution function of the core of this type of submarine cable is obtained by the Gram-Charlier series expansion of the semi-invariant variables of each order, as shown in Figure 2.

表4 YJQ41G-500型海缆线芯温度各阶半不变量Table 4 YJQ41G-500 type submarine cable core temperature semi-invariant of each order

《海底电力电缆运行规程》规定海缆线芯最高运行温度为90℃，图中得到P₅₀₀(T＞90℃)≈0。即YJQ41G-500型海缆在最差工况下线芯温度越限的概率几乎为0，说明其在工程运用中绝对安全。考虑到海缆选型存在负载冗余问题，下面对其它典型110kV海缆进行半不变量法分析。其它型号线芯温度各阶半不变量具体计算结果表5所示。The "Submarine Power Cable Operation Regulations" stipulates that the maximum operating temperature of the submarine cable core is 90°C, and P₅₀₀ (T>90°C)≈0 is obtained from the figure. That is to say, the probability that the core temperature of the YJQ41G-500 submarine cable exceeds the limit under the worst working condition is almost 0, indicating that it is absolutely safe in engineering applications. Considering the problem of load redundancy in the selection of submarine cables, the semi-invariant analysis of other typical 110kV submarine cables is carried out below. Table 5 shows the specific calculation results of each order semi-invariant of core temperature of other models.

表5 YJQ41G-350、400、450型海缆线芯温度各阶半不变量Table 5 YJQ41G-350, 400, 450 type submarine cable core temperature semi-invariant of each order

计算结果表明YJQ41G-450型海缆温度越限的概率同样几乎为0；而YJQ41G-400型海缆温度越限的概率为P₄₀₀(T＞90℃)＝8.5063e-4，根据Gram-Charlier级数展开方法及式(15)、式(16)，便可得到该型号海缆线芯温度累积概率分布函数和概率密度函数曲线，如图3、4所示。图4中，海缆线芯温度属于一种双峰密度函数的分布，可以看成是Weibull分布的推广。The calculation results show that the probability of the YJQ41G-450 type submarine cable temperature exceeding the limit is also almost 0; while the probability of the YJQ41G-400 type submarine cable temperature exceeding the limit is P₄₀₀ (T>90°C) = 8.5063e-4, according to Gram-Charlier Series expansion method and formula (15) and formula (16), the cumulative probability distribution function and probability density function curve of the core temperature of this type of submarine cable can be obtained, as shown in Figures 3 and 4. In Figure 4, the core temperature of the submarine cable belongs to the distribution of a bimodal density function, which can be regarded as an extension of the Weibull distribution.

另外，通过计算分析可得YJQ41G-350温度越限概率为P₃₅₀(T＞90℃)＝0.016。In addition, through calculation and analysis, the probability of temperature violation of YJQ41G-350 is P₃₅₀ (T>90°C)=0.016.

如今，海缆一般埋设在海底以下0.6-2m处。海缆利用其热容量，可以运行短时过负载，时间相对较短，为0.5-2h。本文研究时间周期为一个月，那么，流程图中ε为ε≤2.78×10^-3。Today, submarine cables are generally buried 0.6-2m below the seabed. Utilizing its heat capacity, the submarine cable can run short-term overload, and the time is relatively short, 0.5-2h. The research time period of this paper is one month, then, ε in the flow chart is ε≤2.78×10^-3 .

综上所述，YJQ41G-400、450型海缆均可靠，但YJQ41G-350型可靠性较低，所以实际风电场工程中可舍弃YJQ41G-500型，改选YJQ41G-400型海缆。从而证明了该半不变量法的可行性。To sum up, the YJQ41G-400 and 450 type submarine cables are reliable, but the YJQ41G-350 type is less reliable, so the YJQ41G-500 type can be abandoned in the actual wind farm project, and the YJQ41G-400 type submarine cable can be selected instead. Thus, the feasibility of the semi-invariant method is proved.

Claims (4)

1. a kind of wind energy turbine set send line optimized Selection method it is characterised in that: comprise the following steps:

S1: build power cable thermal circuit model and wind-power electricity generation environmental factorss stochastic model respectively；

S2: build power cable core temperature linearity model, calculate each rank cumulant of each stochastic variable；

S3: the property according to cumulant and definition, try to achieve each rank cumulant of cable core temperature；

S4: combine cable core temperature each rank cumulant with gram-charlier series expansion and obtain state variable coreThe probability density function of temperature and out-of-limit probability, thus be optimized type selecting.

2. wind energy turbine set according to claim 1 send line optimized Selection method it is characterised in that: described step s1 include withLower step:

S1.1: build power cable thermal circuit model；

S1.2: set up wind speed stochastic model；

With weibull distribution function, wind speed is described, shown in the probability density mathematical model such as formula (1) of wind speed:

$f\left(v_w\right)=\frac{k}{c}{\left(\frac{v_w}{c}\right)}^{k-1}{e}^{\&lsqb;-{\left(\frac{v_w}{c}\right)}^k\&rsqb;}---\left(1\right)$

In formula (1), c is scale parameter, and k is form parameter, v_wFor wind speed (m/s)；

The random distribution that wind turbine is exerted oneself is obtained with the approximate once linear relationship between wind speed by the output of wind turbine, itsShown in probability density mathematical model such as formula (2):

$f\left(p_w\right)=\frac{k}{ac}{\left(\frac{p_w+b}{ac}\right)}^{k-1}{e}^{\&lsqb;-{\left(\frac{p_w+b}{ac}\right)}^k\&rsqb;}---\left(2\right)$

In formula (2), p_wFor wind turbine output, a=p_r/(v_r-v_ci), b=p_rv_ci/(v_r-v_ci), p_rFor the specified work(of wind turbineRate, v_rFor wind turbine rated wind speed, v_ciCut wind speed for wind turbine；

By the theorem that weibull is distributed push away cable current probability density function is:

$f\left(i\right)=\frac{dk}{ac}{\left(\frac{(i+b)d}{ac}\right)}^{k-1}{e}^{\&lsqb;-{\left(\frac{(i+b)d}{ac}\right)}^k\&rsqb;}---\left(3\right)$

In formula (3),U is cable voltage class, and cos θ is rated power factor, and n is blower fan number, and i isCable current；

S1.3: set up ambient temperature stochastic model；

Ambient temperature sampled data uses normal distribution, and its probability density function is:

$f\left({\mathrm{\&theta;}}_a\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}{e}^{\&lsqb;-\frac{{({\mathrm{\&theta;}}_a-\mathrm{\&mu;})}^2}{2{\mathrm{\&sigma;}}^2}\&rsqb;}---\left(4\right)$

In formula (4), θ_aFor ambient temperature sampled data, μ is average, σ²For variance；

S1.4: input raw process parameter data, chooses the worst operating mode of combination and is studied.

3. wind energy turbine set according to claim 2 send line optimized Selection method it is characterised in that: described step s2 include withLower step:

S2.1: set up power cable core temperature linearity model；

Cable current mathematical model is:

i²{r[t₁+(1+λ₁)t₂+(1+λ₁+λ₂)(t₃+t₄)]=θ_c-θ_a-w_d[0.5t₁+t₂+t₃+t₄] (5)

In formula (5), i is cable current, and r hinders for cable AC electric, t₁For insulating barrier thermal resistance, t₂For metal screen layer thermal resistance, t₃ForArmor external jacket thermal resistance, t₄For the thermal resistance of cable laying ambient soil, λ₁For cable metal layer loss factor, λ₂For armouringLoss factor, θ_cFor core operating temperature, w_dFor the loss of unit length dielectric,u₀Lead for cableBody voltage-to-ground, w=2 π f, wherein f are supply frequency, and c is the electric capacity of unit length cables, and tan δ is the loss of dielectricAngle tangent；

And formula (5) meets:

δθ_c=2ai₀δi+δθ_a(6)

In formula (6), δ θ_cFor the difference of cable core operating temperature and its expected value, i₀For cable current expected value, δ i is electricityCable electric current and the difference of its expected value, δ θ_aDifference for ambient temperature and its expected value；

S2.2: according to formula (3) and formula (4) by cable current and ambient temperature discretization, then asked by Random Variable Distribution FunctionObtain the probability of each centrifugal pump, and each rank square according to formula (7) calculating current and ambient temperature stochastic variable, further according to formula (8) meterCalculate each rank cumulant；

$m_r=\underset{i}{\&sigma;}{p}_i{(x_i-\mathrm{\&mu;})}^r---\left(7\right)$

In formula (7), m_rFor each rank square of electric current and ambient temperature, 1≤r≤8, p_iFor the probit of electric current and ambient temperature, x_iForElectric current and the centrifugal pump of ambient temperature, μ is the expected value of electric current and ambient temperature, 1≤i≤electric current and ambient temperature centrifugal pumpNumber；

$\begin{array}{c}\begin{array}{ccc}{n}_1=\mathrm{\&mu;}& n_2=m_2& n_3=m_3\end{array}\\ n_4=m_4-3m_2^2\\ n_5=m_5-10m_3{m}_2\\ n_6=m_6-15m_4{m}_2-10m_3^2+30m_2^3\\ n_7=m_7-21m_5{m}_2-35m_4{m}_3+210m_3{m}_2^2\\ n_8=m_8-28m_6{m}_2-56m_5{m}_3-35m_4^2+420m_4{m}_2^2+560m_3^2{m}_2-630m_2^4\end{array}---\left(8\right)$

In formula (8), n_rEach rank cumulant for electric current and ambient temperature.

4. wind energy turbine set according to claim 1 send line optimized Selection method it is characterised in that: the shape in described step s4Probability density function f (x) of state variable core temperature is:

$f\left(x\right)=\mathrm{\&psi;}\left(\stackrel{\&overbar;}{x}\right)+\mathrm{\&psi;}\left(\stackrel{\&overbar;}{x}\right)\&lsqb;\frac{g_3}{3!}{h}_3\left(\stackrel{\&overbar;}{x}\right)+\frac{g_4}{4!}{h}_4\left(\stackrel{\&overbar;}{x}\right)+\frac{g_5}{5!}{h}_5\left(\stackrel{\&overbar;}{x}\right)+\frac{g_6+10g_3^2}{6!}{h}_6\left(\stackrel{\&overbar;}{x}\right)+\frac{g_7+35g_3{g}_4}{7!}{h}_7\left(\stackrel{\&overbar;}{x}\right)+\frac{g_8+56g_3{g}_5+35g_4^2}{8!}{h}_8\left(\stackrel{\&overbar;}{x}\right)+...\&rsqb;---\left(9\right)$

In formula (9),Standard normal density function for state variable core temperature；For the state variable line after normalizationCore temperature, that is,μ is the expectation of state variable core temperature, σ²For the variance of state variable core temperature, g_rFor normalization after cable core temperature each rank cumulant, that is,n_rR for cable core temperatureRank cumulant, 1≤r≤8,For hermite multinomial.