感应电机电压跌落临界清除时间解析算法及应用
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摘要
随着我国工业的蓬勃发展,有越来越多的感应电动机应用于工业生产,其在工业负荷中所占的比例高达90%以上。感应电动机运行良好与否,已经成为影响工业生产连续性的重要因素。而影响感应电动机最主要的电能质量问题就是电压跌落。相关统计数据表明,由电压跌落引起的用户投诉占整个电能质量问题投诉数量的80%以上。电压跌落影响工业感应电动机的主要表现是造成大量的非必要停机。现代高度自动化的工业生产过程一旦中断,将会造成巨大的经济损失甚至危害人身安全。而另一方面,绝大多数电压跌落的幅值都在其额定电压幅值的80%左右且其持续时间仅为4-10周期,考虑到感应电动机及其负载本身所具有的惯性,感应电动机自身有能力穿越这些电压跌落并恢复稳定运行。因此,工业用户有强烈的愿望来改善感应电动机的保护,避免因电压跌落造成生产过程不必要的中断。此外,随着感应发电机的大量装备及电力系统负担的不断加重,感应发电机的大扰动稳定问题和电网的短期电压稳定问题日益突出,迫切需要有效的方法来对这些稳定问题进行快速评估。
要实现这些需求,必须首先快速计算出感应电机在遭遇电压跌落时其能够穿越的最长时间。解析算法因具有物理概念明确、计算速度快等一系列独特优点,是实现快速、准确在线计算的理想选择。因此,从理论上推导出评估感应电机电压跌落穿越能力的解析算法,无疑具有重要的现实意义。
本文在分析了电压跌落持续期间和电压跌落消除后感应电动机的动态响应之后,结合电磁转矩与负载转矩之间的稳定和不稳定平衡交点的概念,提出了感应电动机电压跌落临界清除时间的概念来衡量感应电动机电压跌落穿越的能力。针对电力系统中危害程度最为严重的三相对称电压跌落,分别为恒转矩负载特性、恒功率负载特性和风机类负载特性推导出了各自的感应电动机对称电压跌落临界清除时间解析算法及临界转差率的计算公式。此外还提出了感应电动机绝对安全电压跌落的概念及判断某一对称电压跌落是否是绝对安全的判定方法,以及最小绝对安对称全电压跌落的概念及其计算方法。仿真实验和参数敏感分析仿真实验都证实了对称电压跌落临界清除时间解析算法与绝对安全对称电压跌落判定方法的有效性和准确性。
针对电力系统中出现次数最多的非对称电压跌落,通过分析感应电动机在非对称电压跌落期间的正负序稳态等效电路及其正负序电磁转矩,提出了总电磁转矩的Ⅰ类和Ⅱ类简化表达形式,并利用不同电磁转矩表达式分别为恒转矩负载特性、恒功率负载特性和风机类负载特性推导出了各自的非对称电压跌落临界清除时间解析算法。此外还提出了判断某一非对称电压跌落是否是绝对安全的判定方法。通过仿真实验验证了所提出的感应电动机非对称电压跌落临界清除时间解析算法和绝对安全非对称电压跌落判定方法的有效性和准确性。
为了便于解析算法实际应用于感应电动机的电压跌落保护,本文提出了利用递推最小二乘法来在线辨识电压跌落发生前后感应电动机上游供电网络等效电路的等效参数和感应电动机总体机械负载参数的方法。为辨识非对称故障期间上游供电网络正负序等效参数而提出了获取感应电动机定子正、负序瞬时电压矢量和瞬时电流矢量的方法。为辨识总体机械负载参数利用扩展卡尔曼滤波来估计感应电动机的电磁转矩。之后利用一个实际配电系统模型来模拟配电系统中可能真实发生的故障来仿真验证参数辨识方法和感应电动机电压跌落临界清除时间解析算法的有效性和准确性。
本文最后分析了机端故障发生时和消除时感应发电机暂态电磁过程对临界清除时间的影响。根据暂态电磁转矩公式分析了机端三相金属性故障发生时和消除时因感应电动机电磁暂态过程而造成的加速面积变化及计算方法,并推导出了这两个暂态过程所对应的补偿时间的计算公式。提出了计及感应发电机暂态过程的临界清除时间保守计算解析方法。通过仿真实验验证了所提出考虑感应发电机暂态过程的临界清除时间解析算法的有效性和准确性。
本文提出的感应电机电压跌落临界清除时间解析算法不仅有助于工业用户实现感应电动机电压跌落的智能保护,还可以用于分析、研究感应发电机大扰动稳定性及考虑感应电动机负荷的系统短时电压稳定性等问题,具有重要的理论意义和实用价值。
With the great boom of the industry in our country, more and more induction motors are being equipped in various industrial departments and they have accounted for more than90%of the whole industrial electric power load. The operating status of induction motors will influence the continuity of industrial production. The voltage sag is the most serious problem in power quality that affects induction motors. The statistics show that more than80%of the complaints caused by power quality are voltage sags. Voltage sags can cause a large number of unnecessary out of service of induction motors. The interruptions of modern highly automated industrial production will lead to a sizable economic loss and may endanger the safety of human life. In the other hand, most voltage sags have a magnitude of around80%and the duration of4to10cycles. So induction motors can ride through these voltage sags and recover to normally operation state by themselves with respect to the inertia of induction motors and their mechanical loads. Consequently, there are strong desires of industrial customers to improve the protections of induction motors in order to avoid unnecessary interruptions of production processes caused by voltage sags. In addition, with the giant equipment of induction generators and rising burden of power system, the large-disturbance stability of induction generators and the short-term voltage stability of power systems are becoming increasingly acute and hence effective methods are desired to be developed to fast estimate these stability problems.
In order to achieve these requirements, the longest time that induction machines can ride through voltage sags should be quickly calculated at first. Analytical methods are the most adaptive choice to conduct fast and accurate on-line computation since it has a lot of unique advantages such as clear physical meaning and high computation speed. Therefore, the developing analytical method that can on-line fast estimate the capability of voltage sag ride-through of induction machines is important undoubtedly.
According to the stable and unstable equilibrium points between electromagnetic torque and mechanical load torque, the concept of voltage sag critical clearance time of induction motors is presented to scale the capability of induction motors' low voltage ride-through after analyzing the dynamic response of induction motors during and after voltage sags. For the three-phase symmetrical voltage sags that are most dangerous to power systems, the analytical methods calculating the voltage sag critical clearance time and the algorithms to calculate the critical slip are derived for the constant torque load scenario, the constant power load scenario and fan type load scenario respectively. Additionally, the concept of the absolutely safe voltage sag for induction motors and its judgment method, and the concept of the minimum absolutely safe voltage sag and its calculation method are presented. The effectiveness and accuracy of the proposed analytical method calculating the symmetrical voltage sag critical clearance time and the judgment method to determine whether a symmetrical voltage sag is absolutely safe have been validated through simulations and a parameter sensitivity study.
In power systems, the unsymmetrical voltage sags occur more often than the symmetrical voltage sags. The type I and the type II simplified expressions of the integral electromagnetic torque of induction motors are presented through analyzing the positive and the negative sequence steady-state equivalent circuit and the positive and the negative sequence electromagnetic torque of induction motors during unsymmetrical voltage sags. Using different expressions of the integral electromagnetic torque, the analytical methods that calculate the unsymmetrical voltage sag critical clearance time are derived for the constant torque load scenario, the constant power load scenario and fan type load scenario respectively. Moreover, a judgment method that determines whether unsymmetrical voltage sags are absolutely safe is also presented. The proposed analytical method calculating the unsymmetrical voltage sag critical clearance time and judgment method are verified through simulations.
For the practical application of the proposed analytical method, the equivalent parameters of the induction motors' upstream network equivalent circuit and the parameters of the integral mechanical load of induction motors are on-line identified by recursive least square algorithm. In order to identify the positive and the negative sequence equivalent parameter of the upstream network during unsymmetrical voltage sags, a method gaining the positive and negative sequence instantaneous voltage vectors and current vectors is presented. The electromagnetic torque of induction motors is on-line estimated through the extended Kalman Filtering to identify the parameters of the integral mechanical load of induction motors. The parameter identification methods and the analytical method calculating the critical clearance time of voltage sags are validated through a simulation model which can simulate faults that may occur in real distribution systems.
The impact of the induction generators' transient electromagnetic process during and after faults on the critical clearance time is analyzed finally. The method to calculate the variation of the acceleration area caused by the induction generators' transient electromagnetic process during and after the fault occurring near induction generators is presented according to the transient electromagnetic torque expressions. Then the method calculating the corresponding compensated time is derived. The analytical method that calculates the conservative critical clearance time considering the transient process of induction generators is stated. This conservative, analytical method is verified through simulations.
The proposed analytical method calculating voltage sag critical clearance time of induction machines not only can help industrial customers improve the intelligent protections of induction motors when voltage sags occur, but also can be used to analyze the large-disturbance stability of induction generators and the short-term voltage stability of power systems considering induction motor load. It has great significance in both theory and practice.
要实现这些需求,必须首先快速计算出感应电机在遭遇电压跌落时其能够穿越的最长时间。解析算法因具有物理概念明确、计算速度快等一系列独特优点,是实现快速、准确在线计算的理想选择。因此,从理论上推导出评估感应电机电压跌落穿越能力的解析算法,无疑具有重要的现实意义。
本文在分析了电压跌落持续期间和电压跌落消除后感应电动机的动态响应之后,结合电磁转矩与负载转矩之间的稳定和不稳定平衡交点的概念,提出了感应电动机电压跌落临界清除时间的概念来衡量感应电动机电压跌落穿越的能力。针对电力系统中危害程度最为严重的三相对称电压跌落,分别为恒转矩负载特性、恒功率负载特性和风机类负载特性推导出了各自的感应电动机对称电压跌落临界清除时间解析算法及临界转差率的计算公式。此外还提出了感应电动机绝对安全电压跌落的概念及判断某一对称电压跌落是否是绝对安全的判定方法,以及最小绝对安对称全电压跌落的概念及其计算方法。仿真实验和参数敏感分析仿真实验都证实了对称电压跌落临界清除时间解析算法与绝对安全对称电压跌落判定方法的有效性和准确性。
针对电力系统中出现次数最多的非对称电压跌落,通过分析感应电动机在非对称电压跌落期间的正负序稳态等效电路及其正负序电磁转矩,提出了总电磁转矩的Ⅰ类和Ⅱ类简化表达形式,并利用不同电磁转矩表达式分别为恒转矩负载特性、恒功率负载特性和风机类负载特性推导出了各自的非对称电压跌落临界清除时间解析算法。此外还提出了判断某一非对称电压跌落是否是绝对安全的判定方法。通过仿真实验验证了所提出的感应电动机非对称电压跌落临界清除时间解析算法和绝对安全非对称电压跌落判定方法的有效性和准确性。
为了便于解析算法实际应用于感应电动机的电压跌落保护,本文提出了利用递推最小二乘法来在线辨识电压跌落发生前后感应电动机上游供电网络等效电路的等效参数和感应电动机总体机械负载参数的方法。为辨识非对称故障期间上游供电网络正负序等效参数而提出了获取感应电动机定子正、负序瞬时电压矢量和瞬时电流矢量的方法。为辨识总体机械负载参数利用扩展卡尔曼滤波来估计感应电动机的电磁转矩。之后利用一个实际配电系统模型来模拟配电系统中可能真实发生的故障来仿真验证参数辨识方法和感应电动机电压跌落临界清除时间解析算法的有效性和准确性。
本文最后分析了机端故障发生时和消除时感应发电机暂态电磁过程对临界清除时间的影响。根据暂态电磁转矩公式分析了机端三相金属性故障发生时和消除时因感应电动机电磁暂态过程而造成的加速面积变化及计算方法,并推导出了这两个暂态过程所对应的补偿时间的计算公式。提出了计及感应发电机暂态过程的临界清除时间保守计算解析方法。通过仿真实验验证了所提出考虑感应发电机暂态过程的临界清除时间解析算法的有效性和准确性。
本文提出的感应电机电压跌落临界清除时间解析算法不仅有助于工业用户实现感应电动机电压跌落的智能保护,还可以用于分析、研究感应发电机大扰动稳定性及考虑感应电动机负荷的系统短时电压稳定性等问题,具有重要的理论意义和实用价值。
With the great boom of the industry in our country, more and more induction motors are being equipped in various industrial departments and they have accounted for more than90%of the whole industrial electric power load. The operating status of induction motors will influence the continuity of industrial production. The voltage sag is the most serious problem in power quality that affects induction motors. The statistics show that more than80%of the complaints caused by power quality are voltage sags. Voltage sags can cause a large number of unnecessary out of service of induction motors. The interruptions of modern highly automated industrial production will lead to a sizable economic loss and may endanger the safety of human life. In the other hand, most voltage sags have a magnitude of around80%and the duration of4to10cycles. So induction motors can ride through these voltage sags and recover to normally operation state by themselves with respect to the inertia of induction motors and their mechanical loads. Consequently, there are strong desires of industrial customers to improve the protections of induction motors in order to avoid unnecessary interruptions of production processes caused by voltage sags. In addition, with the giant equipment of induction generators and rising burden of power system, the large-disturbance stability of induction generators and the short-term voltage stability of power systems are becoming increasingly acute and hence effective methods are desired to be developed to fast estimate these stability problems.
In order to achieve these requirements, the longest time that induction machines can ride through voltage sags should be quickly calculated at first. Analytical methods are the most adaptive choice to conduct fast and accurate on-line computation since it has a lot of unique advantages such as clear physical meaning and high computation speed. Therefore, the developing analytical method that can on-line fast estimate the capability of voltage sag ride-through of induction machines is important undoubtedly.
According to the stable and unstable equilibrium points between electromagnetic torque and mechanical load torque, the concept of voltage sag critical clearance time of induction motors is presented to scale the capability of induction motors' low voltage ride-through after analyzing the dynamic response of induction motors during and after voltage sags. For the three-phase symmetrical voltage sags that are most dangerous to power systems, the analytical methods calculating the voltage sag critical clearance time and the algorithms to calculate the critical slip are derived for the constant torque load scenario, the constant power load scenario and fan type load scenario respectively. Additionally, the concept of the absolutely safe voltage sag for induction motors and its judgment method, and the concept of the minimum absolutely safe voltage sag and its calculation method are presented. The effectiveness and accuracy of the proposed analytical method calculating the symmetrical voltage sag critical clearance time and the judgment method to determine whether a symmetrical voltage sag is absolutely safe have been validated through simulations and a parameter sensitivity study.
In power systems, the unsymmetrical voltage sags occur more often than the symmetrical voltage sags. The type I and the type II simplified expressions of the integral electromagnetic torque of induction motors are presented through analyzing the positive and the negative sequence steady-state equivalent circuit and the positive and the negative sequence electromagnetic torque of induction motors during unsymmetrical voltage sags. Using different expressions of the integral electromagnetic torque, the analytical methods that calculate the unsymmetrical voltage sag critical clearance time are derived for the constant torque load scenario, the constant power load scenario and fan type load scenario respectively. Moreover, a judgment method that determines whether unsymmetrical voltage sags are absolutely safe is also presented. The proposed analytical method calculating the unsymmetrical voltage sag critical clearance time and judgment method are verified through simulations.
For the practical application of the proposed analytical method, the equivalent parameters of the induction motors' upstream network equivalent circuit and the parameters of the integral mechanical load of induction motors are on-line identified by recursive least square algorithm. In order to identify the positive and the negative sequence equivalent parameter of the upstream network during unsymmetrical voltage sags, a method gaining the positive and negative sequence instantaneous voltage vectors and current vectors is presented. The electromagnetic torque of induction motors is on-line estimated through the extended Kalman Filtering to identify the parameters of the integral mechanical load of induction motors. The parameter identification methods and the analytical method calculating the critical clearance time of voltage sags are validated through a simulation model which can simulate faults that may occur in real distribution systems.
The impact of the induction generators' transient electromagnetic process during and after faults on the critical clearance time is analyzed finally. The method to calculate the variation of the acceleration area caused by the induction generators' transient electromagnetic process during and after the fault occurring near induction generators is presented according to the transient electromagnetic torque expressions. Then the method calculating the corresponding compensated time is derived. The analytical method that calculates the conservative critical clearance time considering the transient process of induction generators is stated. This conservative, analytical method is verified through simulations.
The proposed analytical method calculating voltage sag critical clearance time of induction machines not only can help industrial customers improve the intelligent protections of induction motors when voltage sags occur, but also can be used to analyze the large-disturbance stability of induction generators and the short-term voltage stability of power systems considering induction motor load. It has great significance in both theory and practice.
引文
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