【电压】电晕效应的电压依赖输电线模型的Matlab实现

✅作者简介热爱科研的Matlab仿真开发者擅长毕业设计辅导、数学建模、数据处理、建模仿真、程序设计、完整代码获取、论文复现及科研仿真。 往期回顾关注个人主页Matlab科研工作室 关注我领取海量matlab电子书和数学建模资料个人信条格物致知,完整Matlab代码获取及仿真咨询内容私信。 内容介绍一、电晕效应概述电晕现象电晕是指在强电场作用下导体表面附近空气发生电离而产生的一种放电现象。在输电线中当导线表面的电场强度超过空气的击穿场强时导线周围的空气会被电离形成导电通道产生电晕。电晕现象通常伴有发光、发热、嘶嘶声以及臭氧生成等现象。电晕的影响电晕会对输电系统产生多方面影响。一方面电晕会造成电能损耗降低输电效率。这种损耗不仅包括直接的能量损失还会因发热等因素导致输电线路的老化加速。另一方面电晕产生的电磁干扰会影响附近的通信系统降低通信质量。此外电晕产生的臭氧等物质可能对环境和人体健康造成一定危害。二、电压依赖的必要性电晕起始电压存在一个临界电压称为电晕起始电压 Vcr当导线电压达到或超过 Vcr 时电晕现象开始出现。不同的输电线路结构、导线参数以及环境条件如气压、湿度等会导致电晕起始电压不同。在设计和运行输电线路时了解电晕起始电压以及电压与电晕特性之间的关系至关重要因为这直接关系到输电线路的电能损耗、电磁干扰等性能指标。三、电晕效应的电压依赖输电线模型构建原理模型的应用构建的电晕效应电压依赖输电线模型可用于输电系统的分析和设计。在系统规划阶段通过该模型可以预测不同电压等级下输电线路的电晕损耗、电磁干扰等性能指标从而优化线路设计选择合适的导线类型、间距以及电压等级以降低电晕效应的负面影响。在运行阶段该模型可以帮助电力系统运营商实时监测和评估电晕对输电线路性能的影响采取相应的措施如调整电压、维护线路等来保证输电系统的安全、高效运行。⛳️ 运行结果 部分代码%{Author: Luis C. Timaná E.R0: series resistance (Ohm/m)L0: series inductance (H/m)C0: shunt capacitance (F/m)L: line length (m)tao: travel time (s)Z0: Characteristic impedance (Ohms)Z: Norton interface impedance (Ohms)R: total line resistance (Ohms)Ik_t_tao, Im_t_tao: historical currents (A)V_crit: Corona inception voltage (V) (value to be optimized)K_C: Constant associated with shunt capacitance (value to be optimized)K_G: Constant associated with shunt resistance (value to be optimized)Reference:- https://www.pscad.com/webhelp-v502-ol/EMTDC/Transmission_Lines/The_Bergeron_Model.htm%}classdef BergeronModelpropertiesR0 {mustBeNumeric}L0 {mustBeNumeric}C0 {mustBeNumeric}L {mustBeNumeric}V_crit {mustBeNumeric}K_C {mustBeNumeric}K_G {mustBeNumeric}endmethods% Constructorfunction obj BergeronModel(values)if nargin 1obj.R0 values(1);obj.L0 values(2);obj.C0 values(3);obj.L values(4);obj.V_crit values(5);obj.K_C values(6);obj.K_G values(7);endendfunction C CalculateCk(obj, vk)if vkobj.V_critC obj.C0;elseC obj.C0 2*obj.K_C*(1 - obj.V_crit/vk);endendfunction tao taoLine(obj, vk_t_deltat)C CalculateCk(obj, vk_t_deltat);tao sqrt(obj.L0*C)*obj.L;endfunction tao taoLineSection(obj, vk_t_deltat , vkp1_t_deltat)% Method 1% C_k CalculateCk(obj, vk_t_deltat);% C_kp1 CalculateCk(obj, vkp1_t_deltat);% C (C_k C_kp1)/2;% tao sqrt(obj.L0*C)*obj.L;% Method 2% tao_k taoLine(obj, vk_t_deltat);% tao_kp1 taoLine(obj, vkp1_t_deltat);% tao (tao_ktao_kp1)/2;% Method 3v_t_deltat (vk_t_deltat vkp1_t_deltat)/2;tao taoLine(obj, v_t_deltat);endfunction Z ZInitialLine(obj)R obj.R0*obj.L;Z0 sqrt(obj.L0/obj.C0);Z Z0R/2;endfunction Z CalculateZLine(obj, vk_t_deltat)if vk_t_deltatobj.V_critZ ZInitialLine(obj);elseR obj.R0*obj.L;Z_0k Calculate_Z(obj, vk_t_deltat);Rsk Calculate_Rs(obj, vk_t_deltat);Z (4*Rsk*Z_0k 2*Rsk*R R*Z_0k) / (4*Rsk 2*Z_0k);endendfunction Z_0kCalculate_Z(obj, v_k)if v_kobj.V_critZ_0k sqrt(obj.L0/obj.C0);elseC_k CalculateCk(obj, v_k);Z_0k sqrt(obj.L0/C_k);endendfunction Rs_kCalculate_Rs(obj, v_k) % This result is valid only if v_kV_critGs_k obj.K_G * (1 - obj.V_crit/v_k)^2;Rs_k 1/(Gs_k*obj.L);endfunction [Ik, Im]historicalCurrents(obj , ikm_t_taom , imk_t_taok , vk_t_taom , vm_t_taok , vk_t_deltat , vm_t_deltat , vk_t_taom_deltat , vm_t_taok_deltat)R obj.R0*obj.L;Z0 sqrt(obj.L0/obj.C0);Z_0m_t_taok Calculate_Z(obj, vm_t_taok_deltat);Z_0k_t_taom Calculate_Z(obj, vk_t_taom_deltat);Rsm_t_taok Calculate_Rs(obj, vm_t_taok_deltat);% This result is valid only if vm_t_taok_deltatobj.V_critRsk_t_taom Calculate_Rs(obj, vk_t_taom_deltat);% This result is valid only if vk_t_taom_deltatobj.V_critRsk_t Calculate_Rs(obj, vk_t_deltat);% This result is valid only if vk_t_deltatobj.V_critRsm_t Calculate_Rs(obj, vm_t_deltat);% This result is valid only if vm_t_deltatobj.V_critZ_0k Calculate_Z(obj, vk_t_deltat);Z_0m Calculate_Z(obj, vm_t_deltat);% Calculation of historical currents Ikif ( vk_t_deltatobj.V_crit vm_t_taok_deltatobj.V_crit )Ik vm_t_taok * ( -2 / (2*Z0R)) imk_t_taok * ( (R-2*Z0) / (R2*Z0));elseif ( vk_t_deltatobj.V_crit vm_t_taok_deltatobj.V_crit )Ik ( 2 / (Rsm_t_taok*(4*Z02*R)) ) * ( vm_t_taok*(-2*Rsm_t_taok Z_0m_t_taok) imk_t_taok*(R*Rsm_t_taok-2*Z_0m_t_taok*Rsm_t_taok-(R/2)*Z_0m_t_taok) );elseif ( vk_t_deltatobj.V_crit vm_t_taok_deltatobj.V_crit )Ik ( (2*Rsk_t) / (4*Rsk_t*Z_0kR*Z_0k2*R*Rsk_t) ) * ( -2*vm_t_taok imk_t_taok*(R-2*Z0) );elsetemp (2*Rsk_t) / ( Rsm_t_taok *(4*Rsk_t*Z_0k R*Z_0k 2*R*Rsk_t));Ik temp * ( vm_t_taok*( -2*Rsm_t_taok Z_0m_t_taok ) imk_t_taok * (R*Rsm_t_taok - 2*Z_0m_t_taok*Rsm_t_taok - (R/2)*Z_0m_t_taok));end% Calculation of historical currents Imif ( vm_t_deltatobj.V_crit vk_t_taom_deltatobj.V_crit )Im vk_t_taom * ( -2 / (2*Z0R)) ikm_t_taom * ( (R-2*Z0) / (R2*Z0));elseif ( vm_t_deltatobj.V_crit vk_t_taom_deltatobj.V_crit )Im ( 2 / (Rsk_t_taom*(4*Z02*R)) ) * ( vk_t_taom*(-2*Rsk_t_taom Z_0k_t_taom) ikm_t_taom*(R*Rsk_t_taom-2*Z_0k_t_taom*Rsk_t_taom-(R/2)*Z_0k_t_taom) );elseif ( vm_t_deltatobj.V_crit vk_t_taom_deltatobj.V_crit )Im ( (2*Rsm_t) / (4*Rsm_t*Z_0mR*Z_0m2*R*Rsm_t) ) * ( -2*vk_t_taom ikm_t_taom*(R-2*Z0) );elsetemp (2*Rsm_t) / ( Rsk_t_taom *(4*Rsm_t*Z_0m R*Z_0m 2*R*Rsm_t));Im temp * ( vk_t_taom*( -2*Rsk_t_taom Z_0k_t_taom ) ikm_t_taom * (R*Rsk_t_taom - 2*Z_0k_t_taom*Rsk_t_taom - (R/2)*Z_0k_t_taom));endendendend 参考文献往期回顾扫扫下方二维码 往期回顾可以关注主页点击搜索