Flexible arc suppression method for single-phase to ground fault in distribution network based on Z-type grounding transformer
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摘要: 煤矿供配电系统通常采用中性点非有效接地方式，该方式下的供电线路多数采用电缆线路，井下供电系统复杂，使用的电压等级较多，发生单相接地故障时极易在接地点形成间歇性电弧。而现有中性点非有效接地配电网单相接地故障消弧技术存在消弧效果不佳、难以精准测量配电网对地参数等问题。我国煤矿10 kV变电站中变压器绕组最常用的接线方式是三角形接线，该方式需通过专用接地变压器（大多是Z型接地变压器）人为引出中性点连接消弧线圈。针对上述情况，设计了一种基于Z型接地变压器的配电网单相接地故障柔性消弧系统。当配电网发生接地故障初始时刻，首先实时测量配电网的三相电源电动势和中性点电压，当中性点电压幅值大于三相电源电动势的15%时，可判断为接地故障；对比三相电源电动势，其中电源电动势最小相为故障相。在单相接地故障发生后，迅速闭合故障相对应的快速投切开关，同时投入有源逆变器和Z型接地变压器功率转换模块，其中Z型接地变压器功率转换模块将中性点电压反相钳制接近于故障相电源电动势，中性点电压与故障相电源电压差值的幅值和相位由有源逆变器精确补偿，实现将故障点电压和电流抑制至零的控制目标。一定时间延时后切除快速投切开关，若中性点电压有效降低则可判断该故障为瞬时性接地故障，即可恢复配电网正常运行，否则判断为永久性故障，采取故障馈线隔离措施，恢复配电网正常运行。仿真结果表明，当单相接地故障过渡电阻为500 Ω和3 000 Ω时，仅通过Z型接地变压器功率转换，故障点电压和电流抑制率达79%~83%，不能完全达到消弧效果；投入柔性消弧系统可有效抑制故障点电压和电流，抑制率达98%以上，实现配电网单相接地故障的可靠消弧。Abstract: The coal mine power supply and distribution system usually adopts the neutral point non-effectively grounded method. Most of the power supply lines in this method use cable lines. The underground power supply system is complex and uses many voltage levels. When a single-phase to ground fault occurs, it is easy to form intermittent arcs at the grounding point. Moreover, the existing single-phase to ground fault arc suppression technology of the neutral point non-effectively grounded distribution network has the problem of poor arc suppression effect and difficulty in accurately measuring the parameters of the distribution network to the ground. The most common connection method of transformer winding in 10 kV substation of coal mine in China is delta connection. This mode needs to lead out neutral point and connect arc suppression coil artificially through special grounding transformer (mostly Z-type grounding transformer). In order to solve the above problems, a flexible arc suppression system for single-phase to ground fault of distribution network based on Z-type grounding transformer is designed. When the initial time of grounding fault occurs in the distribution network, the three-phase power supply electromotive force and the neutral point voltage of the power distribution network are firstly measured in real time. When the amplitude of the neutral point voltage is greater than 15% of the three-phase power supply electromotive force, it can be judged as a grounding fault. Compared with the three-phase power supply electromotive force, the phase with the smallest power supply electromotive force is the fault phase. After a single-phase to ground fault occurs, the fast switching switch corresponding to the fault phase is quickly closed. And the active inverter and the Z-type grounding transformer power conversion module are simultaneously put into operation. The Z-type grounding transformer power conversion module clamps the voltage of a neutral point in an opposite phase to be close to the electromotive force of the fault phase power supply. And the amplitude and the phase of the difference between the neutral voltage and the fault phase supply voltage are precisely compensated by the active inverter. Therefore, the control target of suppressing the voltage and the current at the fault point to zero is achieved. After a certain time delay, the fast switching switch is cut off. If the voltage of the neutral point is effectively reduced, it can be judged that the fault is a transient ground fault. And the normal operation of the power distribution network system can be restored. Otherwise, it is judged as a permanent fault. The measures to isolate the fault feeder are taken to restore the normal operation of the distribution network. The simulation results show that when the single-phase to ground fault transition resistance is 500 Ω and 3 000 Ω, the power conversion is only through the Z-type grounding transformer. The voltage and current suppression rate at the fault point reaches 79%-83%, which cannot fully achieve the effect of arc suppression. The flexible arc suppression system can effectively suppress the voltage and current at the fault point, with a suppression rate of more than 98%, realizing reliable arc suppression of single-phase to ground faults in the distribution network.
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0. 引言
我国煤矿供配电系统通常采用中性点非有效接地方式，该方式在发生单相接地故障时可短暂运行[1]。但中性点非有效接地方式下的供电线路大多采用电缆线路，导致井下供电系统复杂，电压等级较多，发生单相接地故障时对地电容大，导致接地故障过电压产生概率增大，极易在接地点形成间歇性电弧，出现弧光接地过电压，严重时会造成大面积停电，影响电气设备正常运行，危及矿井供电安全及井下工作人员人身安全[2]。若不能快速抑制电弧，易引起超过3倍相电压的系统过电压，会发展为永久性单相接地故障，极易造成相间短路故障[3-4]。当前主要通过中性点经消弧线圈接地或经电阻接地对电弧进行快速抑制。在我国煤矿10 kV变电站中变压器绕组最常用的接线方式是三角形接线，该方式无中性点引出，需通过专用接地变压器人为引出中性点连接消弧线圈，而大多数变电站采用的接地变压器为Z型接地变压器[5]。
影响单相接地故障产生电弧的主要因素包括接地故障电流和间歇性电弧过电压，其中间歇性电弧过电压包括故障相恢复电压的速度、恢复电压幅值和恢复时间 [6-7]。根据影响因素来确定补偿目标，将补偿目标方法（单相接地故障消弧方法）分为电压消弧法和电流消弧法。电压消弧法是指控制故障相恢复电压为零，达到故障残流为零[8]。电流消弧法是指利用中性点接地电抗补偿接地故障残流，降低介质损伤和故障相恢复电压的上升速度，促进故障消弧[8]。
许多学者针对煤矿配电网单相接地故障消弧方法进行了研究。文献[9]通过控制三相级联H桥变流器分相向配电网各相注入电流，以补偿接地故障电流，并抑制故障相电源电压为零，该方法弊端是需解决补偿器件耐压问题，且实现成本较高。文献[10]提出了中性点电阻接地超前相接电感、中性点电抗接地滞后相接电容的方法，该方法难以准确测量配电网对地参数，不能判别故障相，受限于实际应用，操作较复杂。文献[11]在消弧线圈与接地变压器组合的基础上，研制出三相五柱式消弧线圈，采用可控硅调节二次电感电流的方法，实现配电网对地电容电流的自动跟踪补偿，但该方法的消弧效果不佳。文献[12]在零序电压柔性控制的配电网接地故障消弧与保护新原理的基础上，提出了一种配电网三相不对称电压抑制的新原理，故障初期通过脉宽调制有源逆变器注入零序电流补偿接地故障电流，从而控制零序电压，实现瞬时故障消弧，但该方法配备的有源逆变器容量大、成本高且体积大。
针对现有中性点非有效接地配电网单相接地故障消弧方法的消弧效果不佳、难以精准测量配电网对地参数等问题，设计了一种基于Z型接地变压器的配电网单相接地故障柔性消弧系统。当配电网发生接地故障时，测量配电网电压和中性点电压，判断出故障相后迅速闭合其对应的快速投切开关，同时投入有源逆变器与Z型接地变压器功率转换模块，进而使中性点电压反相钳位至故障相电源电压，且二者幅值相等，即可达到故障点稳定消弧的目标。
1. 基本原理
1.1 Z型接地变压器原理
接地补偿电流本质上是零序电流，而接地变压器由于特殊的连结方式，具有非常小的零序阻抗特点，使零序电流可正常流过接地变压器[13]。柔性消弧系统中接地变压器Zn，yn11接线方式如图1所示，图中X1，X2，X3分别为Z型接地变压器高压侧与中性点非有效接地系统连接的一端，X4，X5，X6分别为Z型接地变压器高压侧与中性点接消弧线圈相连的一端，a，b，c分别为Z型接地变压器低压侧。Z型接地变压器的三相绕组按Z型连接，且各相芯柱中的2段绕组匝数相同、极性相反。当配电网发生单相接地故障时，该接地变压器对正序和负序电流产生非常大的阻抗，流过的正序、负序电流较小。同时，同一芯柱上的2段绕组流过相等的零序电流而产生相互抵消的磁通，对零序电流产生低阻抗，可使系统零序电流正常通过[13]。Z型接地变压器可满足系统对零序阻抗小的要求，能够更好地配合消弧线圈使用，同时可使零序接地保护正确动作。
1.2 柔性消弧系统原理
柔性消弧系统原理如图2所示，其中，配电网系统主变压器为Y−∆连接，EA，EB，EC分别为A，B，C三相线路电源电动势，RA，RB，RC分别为A，B，C三相线路对地电阻，CA，CB，CC分别为A，B，C三相线路对地电容， Z0为消弧线圈阻抗，Y0为中性点接地导纳，Yf为接地故障导纳。GLB为隔离变压器，ZRB为注入变压器。
假设A相发生单相接地故障，由基尔霍夫定律可得
$$ \begin{split} {{\boldsymbol{I}}_1} =& \left( {{Y_{\text{A}}} + {Y_{\text{f}}}} \right)({{\boldsymbol{E}}_{\text{A}}} + {{\boldsymbol{U}}_{\text{N}}}) + {Y_{\text{B}}}({{\boldsymbol{E}}_{\text{B}}} + {{{{\boldsymbol{U}}}}_{\text{N}}}) +\\& {Y_{\text{C}}}\left( {{{\boldsymbol{E}}_{\text{C}}} + {{\boldsymbol{U}}_{\text{N}}}} \right) + {Y_{\text{0}}}{{\boldsymbol{U}}_{\text{N}}} \end{split}$$ (1) $$ \left\{ \begin{gathered} Y_{\text{A}} = {\text{j}}\omega C_{\text{A}} + \frac{1}{{R_{\text{A}}}} \hfill \\ Y_{\text{B}} = {\text{j}}\omega C_{\text{B}} + \frac{1}{{R_{\text{B}}}} \hfill \\ Y_{\text{C}} = {\text{j}}\omega C_{\text{C}} + \frac{1}{{R_{\text{C}}}} \hfill \\ Y_{\text{f}} = \frac{1}{{R_{\text{f}}}} \hfill \\ Y_{\text{0}} = \frac{1}{{Z_{\text{0}}}} \hfill \\ \end{gathered} \right. $$ (2) 式中：I1为零序电流；YA，YB，YC分别为A，B，C三相线路总导纳；UN为中性点电压；Rf为接地故障电阻。
假设三相电源对称，即
$$ {\boldsymbol{E}}_{{\rm{A}}}{\text{ + }}{\boldsymbol{E}}_{{\rm{B}}}{\text{ + }}{\boldsymbol{E}}_{{\rm{C}}}{\text{ = 0}} $$ (3) $$ {Y_{\text{A}}} = {Y_{\text{B}}} = {Y_{\text{C}}} $$ (4) 则式（1）可化简为
$$ {{\boldsymbol{I}}_1} = \left( {{Y_{\text{A}}} + {Y_{\text{B}}} + {Y_{\text{C}}}} \right){{\boldsymbol{U}}_{\rm{N}}} + {Y_{\text{0}}}{{\boldsymbol{U}}_{\rm{N}}} + {Y_{\text{f}}}\left( {{{\boldsymbol{E}}_{\text{A}}} + {{\boldsymbol{U}}_{\rm{N}}}} \right) $$ (5) 故障相电源电压为
$$ {\boldsymbol{U}}_{A}{\text{ = }}{\boldsymbol{U}}_{{\rm{N}}}{\text{ + }}{\boldsymbol{E}}_{A} $$ (6) 当
${\boldsymbol{I}}_{1}{{ = 3Y}}_{{\rm{A}}}{\boldsymbol{U}}_{{\rm{N}}}{{ + Y}}_{0}{\boldsymbol{U}}_{{\rm{N}}}$ 时，可得${\boldsymbol{U}}_{{\rm{A}}}{\text{ = }}0$ ，即$$ {\boldsymbol{U}}_{\text{N}} = - {\boldsymbol{E}}_{{\rm{A}}} $$ (7) 向中性点注入零序电流I1即可将故障相电源电压UA降低为零，但该方法需精确测量配电网对地参数。考虑到系统对地参数难以精确测量，因此采用式（7）控制目标，达到故障点可靠消弧。
当系统发生A相单相接地故障时，根据接地变压器高低压侧关系可知，Z型接地变压器低压侧c，a相电压−Uca相位与故障相电源电压UA相位一致，此时有源逆变器输出电压
$ {\boldsymbol{U }}= - {{\boldsymbol{U}}_{{\text{ca}}}} + $ $ \lambda {{\boldsymbol{U}}_{\text{N}}} $ ，λ为ZRB变比。调控有源逆变器输出电压，使中性点电压等于故障相电源电动势的相反数，实现故障点电压远小于熄弧电压，达到接地故障消弧。2. 柔性消弧系统流程
柔性消弧系统流程如图3所示。当配电网发生接地故障时，首先实时测量配电网的三相电源电动势和中性点电压，当中性点电压幅值大于三相电源电动势的15%时，可判断为接地故障；对比三相电源电动势，其中电源电动势最小相为故障相。在单相接地故障发生后，迅速闭合故障相对应的快速投切开关，同时投入有源逆变器和Z型接地变压器功率转换，强制使中性点电压与故障相电源电动势呈等幅值反相位，进而达到故障消弧。一定时间延时后切除快速投切开关，若中性点电压有效降低，则可判断该故障为瞬时性接地故障，即可恢复配电网正常运行，否则判断为永久性故障，采取故障馈线隔离措施，恢复配电网正常运行。
3. 仿真分析
通过Matlab/Simulink模块搭建10 kV中性点非有效接地配电网单相接地故障仿真模型，如图4所示，图中If为故障点电流，Uf为故障点电压。Z型接地变压器高压侧一端在中性点非有效接地系统侧做Z型接线后引出中性点N，再经消弧线圈Lp接地。ZRB变比λ=6 000∶400，Z型接地变压器高低压侧变比λ1=10 000∶400，GLB变比λ2=1 000∶200。
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图 4 中性点非有效接地配电网单相接地故障仿真模型Figure 4. Simulation model of single-phase to ground fault of neutral point non-effectively grounded distribution network3.1 Z型接地变压器功率转换
Z型接地变压器功率转换是指利用Z型接地变压器对故障相电源电压进行反相钳位补偿。模拟接地故障过渡电阻为500，3 000 Ω的单相接地故障，仿真波形如图5—图8所示，仿真结果见表1。仿真时间为0.4 s，在0.05 s时发生A相接地故障，0.1 s时投入Z型接地变压器功率转换。
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图 5 故障相电源电压相反数和中性点电压仿真波形(过渡电阻500 Ω)Figure 5. Simulation waveforms of the opposite number of the fault phase power supply voltage and the neutral point voltage (transition resistance 500 Ω)![]()
图 8 故障点电压、故障点电流和消弧装置注入电流仿真波形(过渡电阻3 000 Ω)Figure 8. Simulation waveforms of fault point voltage, fault point current and injection current of arc suppression device (transition resistance 3 000 Ω)表 1 不同过渡电阻下仿真结果Table 1. Simulation results under different transition resistances过渡电阻/Ω −EA/V UN/V Uf/V If/A I1/A 500 未投 5 759 4 810 3 032 6.06 无 投入 5 759 5 854 649 1.30 2.42 3 000 未投 5 759 1 530 5 169 1.73 − 投入 5 759 5 841 910 0.30 3.36 由图5可知，当0.05 s发生A相接地故障且过渡过渡电阻为500 Ω时，中性点电压有效值（最大值与有效值的比值为
$ \sqrt 2 $ ）为4 810 V，故障相电源电压相反数有效值为5 759 V，二者在幅值和相位上存在一定偏差；在0.1 s投入Z型接地变压器功率转换后，中性点电压幅值在0.17 s后迅速追上故障相电源电压。由图6可知，当0.05 s发生故障时，故障点电压有效值为3 032 V，故障点电流有效值为6.06 A。通过Z型接地变压器功率转换0.17 s后，故障点电压有效值为649 V，抑制率达79%；故障点电流有效值为1.3 A，抑制率达79%。
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图 6 故障点电压、故障点电流和消弧装置注入电流仿真波形(过渡电阻500 Ω)Figure 6. Simulation waveforms of fault point voltage, fault point current and injection current of arc suppression device (transition resistance 500 Ω)由图7可知，当0.05 s发生A相接地故障且过渡电阻为3 000 Ω时，中性点电压有效值为1 530 V，故障相电源电压相反数有效值为5 759 V，二者在幅值和相位上存在一定偏差；在0.1 s投入Z型接地变压器功率转换后，中性点电压幅值在0.18 s后迅速追上故障相电源电压。
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图 7 故障相电源电压相反数和中性点电压仿真波形(过渡电阻3 000 Ω)Figure 7. Simulation waveforms of the opposite number of the fault phase power supply voltage and the neutral point voltage (transition resistance 3 000 Ω)由图8可知，当0.05 s发生故障时，故障点电压有效值为5 169 V，故障点电流有效值为1.73 A。通过Z型接地变压器功率转换0.18 s后，故障点电压有效值为910 V，抑制率达82%；故障点电流有效值为0.30 A，抑制率达83%。
说明当系统发生单相接地故障时，通过Z型接地变压器功率转换可有效降低故障点电压和故障点电流。但降低后的故障点电压仍高达600 V以上，尚未完全达到消弧效果，且易发生触电事故，煤矿操作人员仍不能实现不停电作业。
3.2 柔性消弧系统
消弧线圈只能补偿故障残流中的无功残流，引入有源逆变器对故障残流中的有功残流和谐波残流进行精确补偿。有源逆变器容量仅为10 kVA，通过Z型接地变压器功率转换，将中性点电压反相钳制接近于故障相电源电压，中性点电压与故障相电源电压差值的幅值和相位由有源逆变器补偿。模拟接地故障过渡电阻为500，3 000 Ω的单相接地故障，仿真波形如图9—图12所示，仿真结果见表2。仿真时间为0.4 s，0.05 s时发生A相接地故障，0.1 s时投入柔性消弧系统。
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图 9 故障相电源电压相反数和中性点电压仿真波形(过渡电阻500 Ω)Figure 9. Simulation waveforms of the opposite number of the fault phase power supply voltage and the neutral point voltage(transition resistance 500 Ω)![]()
图 12 故障点电压、故障点电流和柔性消弧系统注入电流仿真波形(过渡电阻3 000 Ω)Figure 12. Simulation waveforms of fault point voltage, fault point current and injection current of flexible arc suppression system (transition resistance 3 000 Ω)表 2 不同过渡电阻下仿真结果Table 2. Simulation results under different transition resistances过渡电阻/Ω −EA/V UN/V Uf/V If/A I1/A 500 未投 5 759 4 810 3 032 6.06 无 投入 5 759 5 765 61.06 0.12 3.49 3000 未投 5 759 1 530 5 169 1.73 无 投入 5 759 5 852 62.79 0.02 3.55 由图9可知，当0.05 s发生A相接地故障且过渡电阻为500 Ω时，中性点电压有效值为4 810 V，故障相电源电压相反数有效值为5 759 V，二者在幅值和相位上存在一定偏差；在0.1 s投入柔性消弧系统后，中性点电压有效值为5 765 V，故障相电源电压相反数有效值为5 759 V，中性点电压的幅值和相位在0.16 s后迅速追上故障相电源电压。
由图10可知，当0.05 s发生A相接地故障时，故障点电压有效值为3 032 V，故障点电流有效值为6.06 A。投入柔性消弧系统0.16 s后，故障点电压有效值为61.06 V，抑制率达98%；故障点电流有效值为0.12 A，抑制率达98%。
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图 10 故障点电压、故障点电流和柔性消弧系统注入电流仿真波形(过渡电阻500 Ω)Figure 10. Simulation waveforms of fault point voltage, fault point current and injection current of flexible arc suppression system(transition resistance 500 Ω)由图11可知，当0.05 s发生A相接地故障且过渡电阻为3 000 Ω时，中性点电压有效值为1 530 V，故障相电源电压相反数有效值为5 759 V，二者在幅值和相位上存在一定偏差；在0.1 s投入柔性消弧系统后，中性点电压有效值为5 852 V，故障相电源电压相反数有效值为5 759 V，中性点电压的幅值和相位在0.17 s后迅速追上故障相电源电压。
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图 11 故障相电源电压相反数和中性点电压仿真波形(过渡电阻3 000 Ω)Figure 11. Simulation waveforms of the opposite number of the fault phase power supply voltage and the neutral point voltage(transition resistance 3 000 Ω)由图12可知，当0.05 s发生A相接地故障时，故障点电压有效值为5 169 V，故障点电流有效值为1.73 A。投入柔性消弧系统0.17 s后，故障点电压有效值为62.79 V，抑制率达99%；故障点电流有效值为0.02 A，抑制率达99%。
相对仅通过Z型接地变压器功率转换，采用柔性消弧系统可有效提高故障抑制率，消弧效果好且响应速度快。由于加入了有源逆变器对中性点电压和故障相电源电压相反数的差值进行精确补偿，使故障残流产生的有功残流和谐波残流得到充分补偿，实现了不同过渡电阻下故障消弧目标。
4. 结语
针对当前中性点非有效接地配电网单相接地故障消弧问题，设计了基于Z型接地变压器的配电网单相接地故障柔性消弧系统。通过Z型接地变压器功率转换，将中性点电压反相钳制接近于故障相电源电压，中性点电压与故障相电源电压差值偏差电压的幅值和相位由有源逆变器补偿。仿真结果表明，单相接地故障过渡电阻为500，3 000 Ω时，仅通过Z型接地变压器功率转换，故障点电压和电流抑制率达79%~83%，不能完全达到消弧效果；采用柔性消弧系统可有效抑制故障点电压和电流，抑制率达98%以上。说明基于Z型接地变压器的配电网单相接地故障柔性消弧系统可实现配电网单相接地故障的可靠消弧。
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图 4 中性点非有效接地配电网单相接地故障仿真模型
Figure 4. Simulation model of single-phase to ground fault of neutral point non-effectively grounded distribution network
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图 5 故障相电源电压相反数和中性点电压仿真波形(过渡电阻500 Ω)
Figure 5. Simulation waveforms of the opposite number of the fault phase power supply voltage and the neutral point voltage (transition resistance 500 Ω)
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图 8 故障点电压、故障点电流和消弧装置注入电流仿真波形(过渡电阻3 000 Ω)
Figure 8. Simulation waveforms of fault point voltage, fault point current and injection current of arc suppression device (transition resistance 3 000 Ω)
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图 6 故障点电压、故障点电流和消弧装置注入电流仿真波形(过渡电阻500 Ω)
Figure 6. Simulation waveforms of fault point voltage, fault point current and injection current of arc suppression device (transition resistance 500 Ω)
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图 7 故障相电源电压相反数和中性点电压仿真波形(过渡电阻3 000 Ω)
Figure 7. Simulation waveforms of the opposite number of the fault phase power supply voltage and the neutral point voltage (transition resistance 3 000 Ω)
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图 9 故障相电源电压相反数和中性点电压仿真波形(过渡电阻500 Ω)
Figure 9. Simulation waveforms of the opposite number of the fault phase power supply voltage and the neutral point voltage(transition resistance 500 Ω)
![]()
图 12 故障点电压、故障点电流和柔性消弧系统注入电流仿真波形(过渡电阻3 000 Ω)
Figure 12. Simulation waveforms of fault point voltage, fault point current and injection current of flexible arc suppression system (transition resistance 3 000 Ω)
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图 10 故障点电压、故障点电流和柔性消弧系统注入电流仿真波形(过渡电阻500 Ω)
Figure 10. Simulation waveforms of fault point voltage, fault point current and injection current of flexible arc suppression system(transition resistance 500 Ω)
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图 11 故障相电源电压相反数和中性点电压仿真波形(过渡电阻3 000 Ω)
Figure 11. Simulation waveforms of the opposite number of the fault phase power supply voltage and the neutral point voltage(transition resistance 3 000 Ω)
表 1 不同过渡电阻下仿真结果
Table 1 Simulation results under different transition resistances
过渡电阻/Ω −EA/V UN/V Uf/V If/A I1/A 500 未投 5 759 4 810 3 032 6.06 无 投入 5 759 5 854 649 1.30 2.42 3 000 未投 5 759 1 530 5 169 1.73 − 投入 5 759 5 841 910 0.30 3.36 
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表 2 不同过渡电阻下仿真结果
Table 2 Simulation results under different transition resistances
过渡电阻/Ω −EA/V UN/V Uf/V If/A I1/A 500 未投 5 759 4 810 3 032 6.06 无 投入 5 759 5 765 61.06 0.12 3.49 3000 未投 5 759 1 530 5 169 1.73 无 投入 5 759 5 852 62.79 0.02 3.55
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