1 引言
2 GIS设备的暂态电路模型
某1 000kV特高压变电站,高压配电装置采用GIS,出线端布置并联电抗器和线路终端设备。
1 000kV高压侧采用双母线分段接线,每段母线各安装避雷器。电气主接线图如图1所示。
图1
2.1 隔离开关的电弧模型
如上述,目前在VFTO的计算中,常用的两种隔离开关的电弧模型是定值电阻模型和时变电阻模型。其中时变电阻模型是将电弧等效为一个时变电阻的形式,即电弧电阻用指数函数近似为
式中,R0 = 1012Ω;T = 1ns;Ra = 0.5Ω。
分段电弧模型中不考虑电流过零后弧隙上的恢复电压,熄弧过程中电弧电阻R是以指数曲线上升,表示为
式中,T = 1ns;Ra0为电弧熄弧临界点弧道电阻;Ra = 0.5Ω。
时变电阻模型在仿真中的模型搭建如图2所示。
图2
图2中,MODEL ARC自定义电弧电阻;R(t)为实时电弧电阻。
2.2 虚拟电感电弧模型
定值电阻模型、时变电阻模型都是纯电阻电弧模型,没有考虑电弧电感特性的阻尼作用,而VFTO频率很高,电弧电感阻尼作用对VFTO的影响较大,文献[5]在定值电阻模型和时变电阻模型的基础上,利用等效阻抗的思想,提出了考虑弧道电感特性的电弧电阻模型,用变化的电感追踪时变的电弧电阻,其阻抗模型为
式中,R为定值电阻;L为电感;X为电抗。由欧拉公式可转换为
对比式（1）〜式（3）可知,式（1）与式（2）可看成只有实部的阻抗式,并且三式均是以指数形式变化。通过不断改变式（3）中L的值,进而改变电抗X值,理论上可以追踪到式（1）与式（2）中预击穿和熄弧阶段电弧电阻的变化趋势。考虑到时变电感会影响系统的稳定性,该模型在仿真中的实现是取某一时刻的静态电感值来实现的,并没有完成动态电感的具体实现,故本文不针对此模型进行对比研究。
本文提出的虚拟电感电弧模型,是在考虑弧道电感特性的电弧电阻模型基础上推导而来,是为了解决考虑弧道电感特性的电弧电阻模型中动态电感难以搭建并且影响系统稳定性的问题,其等效阻抗为
式中,R为定值电阻,取0.5Ω;L(t)为时变电感;ω为角速度。
将式（5）变化为
由角速度、频率的关系得
将杂散电感考虑进虚拟时变电感[6]
式中,f为频率;C为充电电容。
由式（6）~式（8）可推出
对比式（1）和式（9）,利用等效阻抗思想可得到虚拟时变电感L(t)
2.3 虚拟电感电弧模型的模型搭建
图3
等值电流源为
L的等值电阻RL为
由式（12）得到虚拟电感电弧模型的等值电阻为
鉴于以上分析,本文提出的虚拟电感电弧电阻模型按图4搭建的方法实现。
图4
图4中,MODEL ARC为自定义等效电阻,MODEL ARC1为自定义等值电流源,U1、U2为电弧电阻两端电压、MODEL ARC1的输入;R(t)为实时电弧电阻,MODEL ARC输出。MODEL ARC的电弧电阻输出也是MODEL ARC1的输入。
2.4 GIS其他设备的计算模型
计算中电压采用标幺值,基准取系统最高运行相电压峰值,即
3 VFTO的计算与分析
隔离开关操作时触头间隙会发生多次重燃,每次重燃都可能引起VFTO。幅值较大的VFTO在触头间距较大时产生,但两次幅值较大的重燃之间几乎无重叠,上次重燃只决定了下次重燃时空载母线的残压。因此,本文只考虑1次电弧过程中产生的VFTO,不考虑多次重燃[14]。
图5
图5
两种电弧模型下变压器处的VFTO
Fig.5
The VFTO of transformer under two kinds of arc model
由图5可以看出,虚拟电感电弧模型与时变电弧模型下变压器处VFTO曲线吻合得较好,曲线在极值点处略微不同,其中虚拟电感电弧模型下的极值点略高。
GIS设备绝缘主要受VFTO高幅值特性的影响,表1列出了虚拟电感电弧模型下与其他电弧模型在GIS关键设备处VFTO的极值的对比。
表1 GIS各关键设备处VFTO的极值
Tab. 1
| 节点位置 | VFTO幅值(pu) | ||
|---|---|---|---|
| 定值电阻模型 | 时变电阻模型 | 虚拟电感模型 | |
| 变压器 | 1.069 8 | 1.149 7 | 1.150 2 |
| 变压器QS | 2.085 1 | 2.034 5 | 1.983 4 |
| 操作QS | 1.675 3 | 1.708 8 | 1.708 8 |
| 母线端部 | 2.423 1 | 2.639 0 | 2.519 3 |
由表1可以看出,虚拟电感电弧模型与时变电阻电弧模型在GIS内部关键设备处VFTO的极值水平持平,其中时变电阻电弧模型在个别点略微高于虚拟电感电弧模型。定值电阻模型下GIS内部关键设备处VFTO的极值总体偏小。
分析了虚拟电感电弧模型与时变电阻电弧模型下操作隔离开关处的VFTO波形的频谱分布,如图6所示。
图6
图6
两种电弧模型下操作隔离开关处的VFTO 频谱分析图
Fig.6
VFTO Spectrum analysis diagram of isolatingswitch under different arc model
可以看出,两种模型振荡频率基本相同,主要有1MHz左右的基本振荡、10~40MHz左右的高频振荡、60~80MHz和90~100MHz的特高频振荡组成。
表2 不同步长下VFTO的极值
Tab. 2
| 步长/ns | 节点位置 | ||
|---|---|---|---|
| 变压器 | 操作QS | 母线端部 | |
| 0.5 | 1.152 | 1.769 | 2.642 |
| 1 | 1.150 | 1.709 | 2.519 |
| 1.5 | 1.146 | 1.699 | 2.496 |
| 2.0 | 1.141 | 1.724 | 2.364 |
| 2.5 | 1.135 | 1.750 | 2.343 |
图7
由图7分析可知,虚拟电感电弧模型受仿真步长的影响明显,随着仿真步长的增大,变压器和母线端部处VFTO的极值有规律地逐渐变小,而操作隔离开关处的VFTO随着仿真步长的增大呈先减小后增大的不规律现象,这是由操作速度等操作因素的影响造成的。
4 结语
本文提出了虚拟电感电弧模型,并结合某1 000kV GIS变电站,与其他电弧模型进行对比,对GIS内部的VFTO进行了详细计算,结果表明：
（1）虚拟电感电弧模型下得到的变压器处的VFTO波形和时变电阻模型下得到的VFTO波形基本吻合。
（2）虚拟电感电弧模型与时变电阻电弧模型在GIS内部关键设备处VFTO的极值水平持平,其中时变电阻电弧模型在个别点略微高于虚拟电感电弧模型。定值电阻模型下GIS内部关键设备处VFTO的极值总体偏小。
（3）虚拟电感电弧模型与时变电阻电弧模型两种模型振荡频率基本相同,主要有1MHz左右的基本振荡、10~40MHz左右的高频振荡、60~80MHz和90~100MHz的特高频振荡组成。
（4）虚拟电感电弧模型受仿真步长的影响明显,随着仿真步长的增大,变压器和母线端部处VFTO的极值有规律地逐渐变小,而操作隔离开关处的VFTO随着仿真步长的增大呈现先减小而后增大的不规律现象,这是由操作速度等其他操作因素的影响造成的。
综合以上结论,结果表明：虚拟电感模型是考虑弧道电感特性的电弧电阻模型的继续,相比于时变电阻模型和定值电阻电弧模型,考虑了弧道电感特性,并且解决了考虑弧道电感特性的电弧电阻模型中动态电感难以搭建并且影响系统稳定性的问题,在VFTO的计算和分析中,适合在考虑电弧电感特性时使用。
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[J].The exact transient circuit model of gas insulated switchgear (GIS) can directly affect the accuracy of very fast transient overvoltage (VFTO) results in case of calculation. Taking a 1 100 kV GIS substation in China as example, a model symbolizing the transmitting characteristics of GIS enclosure is formed on the basis of theory of multi-conductor transmission lines and phase-model transformation method. By combining above model with the internal transient circuit model of GIS, the VFTO produced by operation of disconnector is calculated and analyzed in details such as the maximum value, spectrum characteristics and rising rate of VFTO on the principal devices inside GIS. Besides, the effect of residual voltage on unoperated phase bus on VFTO of operated phase is also discussed. The calculation and research results could be used as reference for electrical design of GIS and those electric devices connected with it.
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[J].The exact transient circuit model of gas insulated switchgear (GIS) can directly affect the accuracy of very fast transient overvoltage (VFTO) results in case of calculation. Taking a 1 100 kV GIS substation in China as example, a model symbolizing the transmitting characteristics of GIS enclosure is formed on the basis of theory of multi-conductor transmission lines and phase-model transformation method. By combining above model with the internal transient circuit model of GIS, the VFTO produced by operation of disconnector is calculated and analyzed in details such as the maximum value, spectrum characteristics and rising rate of VFTO on the principal devices inside GIS. Besides, the effect of residual voltage on unoperated phase bus on VFTO of operated phase is also discussed. The calculation and research results could be used as reference for electrical design of GIS and those electric devices connected with it.
