电力系统时滞小扰动稳定性研究
发布时间：2019-04-02 04:52
【摘要】：随着我国电网规模的不断扩大和互联程度的不断提高,电网运行的安全性与稳定性面临越来越大的挑战,相关问题受到电力工业界和学术界的高度关注。为提高电力系统运行的安全稳定性水平,利用广域量测系统(WAMS)对其进行协调控制成为一种未来可能的选择,但广域量测系统信息在传输中存在着明显的时滞,会对电力系统的稳定运行和相关控制器的设计产生负面影响,需要加以科学考虑。为此,本文将针对含有时滞环节的电力系统小扰动稳定性开展研究,主要工作如下:(1)在详细推导电力系统关键环节和设备数学模型基础上,利用线性化技术得到了进行时滞电力系统小扰动稳定分析所需的定常模型用于后续研究,包括:典型二阶时滞系统模型、单机-无穷大系统模型、WSCC-3机9节点系统模型和IEEE-10机39节点系统模型。(2)提出了一种求解电力系统大范围时滞小扰动稳定域的有效方法:首先利用参数变换技术,将大范围时滞小扰动稳定域边界的求解,转换为对有限参数空间的搜索、平移和反平移过程,大大减少了稳定域边界的求解量;进一步,利用四点插值法,通过对稳定域边界上临界点实施微扰来确定小扰动稳定域的边界性质和构成;最后,利用典型二阶时滞系统和WSCC-3机9节点时滞系统验证了所给方法的有效性。(3)提出了一种适用于单时滞电力系统模型的简化方法并推导了适用的线性矩阵不等式(LMI)新判据:首先将包含时滞环节的电力系统线性模型,扩展为包含输入-输出环节的状态空间表达式;进一步,利用基于状态空间表达式的降维方法,对扩展后的模型进行简化,在保留系统关键动态基础上尽量减少待求变量数;最后,基于简化模型,推导了新的更为高效的时滞稳定LMI判据。将该方法应用于含时滞环节的WSCC-3机9节点系统和IEEE-10机39节点系统,借助二分搜索算法对比了两种电力系统单时滞稳定裕度的求解结果,算例表明时滞系统经过模型简化后,在保证计算精度的前提下,计算效率大大提升。(4)提出了一种适用于多时滞系统且具有更高求解效率的时滞稳定LMI新判据:首先,通过构造新的Lyapunov-Krasovskii泛函,并通过变分学方法直接得到该泛函导数取极大值的条件,从而形成新的LMI判据,在此过程中避免引入任何自由权矩阵,有效减少了判据的待求变量数;进一步,从理论上证明了新判据的极值条件与已有自由权矩阵判据的最优值等价;最后,利用典型二阶时滞系统、单机-无穷大系统和WSCC-3机9节点系统,验证了所提方法的有效性,计算结果表明新判据在求解相同时滞稳定裕度的情况下,计算效率得到大大提升。
[Abstract]:With the continuous expansion of power grid scale and the continuous improvement of interconnection degree, the security and stability of power grid operation are facing more and more challenges, and the related problems have been highly concerned by the power industry and academia. In order to improve the security and stability of power system operation, the coordinated control of wide area measurement system (WAMS) is a possible choice in the future, but there is obvious time delay in the transmission of wide area measurement system information. It will have a negative effect on the stable operation of the power system and the design of the related controllers, which need to be considered scientifically. The main work of this paper is as follows: (1) on the basis of deducing the key link and equipment mathematical model of power system in detail, the stability of power system with time-delay is studied in this paper. By means of linearization technique, the steady state model needed for small disturbance stability analysis of time-delay power system is obtained for further study, including: typical second-order time-delay system model, single-machine-infinite bus system model, and so on. WSCC- 3 machine 9-bus system model and IEEE- 10 machine 39-bus system model. (2) an effective method to solve the stability region of large-scale time-delay and small disturbance in power system is proposed. Firstly, the parameter transformation technique is used to solve the stability region of power system with time-delay and small disturbance. The solution of the boundary of the stability region with large time-delay and small disturbance is transformed into the search, translation and inverse translation of the finite parameter space, which greatly reduces the solution of the boundary of the stability region. Furthermore, by using the four-point interpolation method, the boundary properties and composition of the small perturbation stability region are determined by perturbing the critical points on the boundary of the stability region. Last, The effectiveness of the proposed method is verified by using the typical second-order time-delay system and the WSCC- 3 machine 9-node time-delay system. (3) A simplified method for single time-delay power system model is proposed and the applicable linear matrix is derived. The new criterion of inequality (LMI): first of all, the linear model of power system with time-delay links is proposed. Extend to include input-output link state space expression; Furthermore, the extended model is simplified by using the dimensionality reduction method based on the state space expression, and the number of variables to be solved is reduced as much as possible on the basis of retaining the key dynamics of the system. Finally, based on the simplified model, a new and more efficient delay-stable LMI criterion is derived. The method is applied to WSCC- 3-machine 9-bus system with time-delay and 39-bus system with IEEE- 10 machine. The results of single-delay stability margin of two power systems are compared by using binary search algorithm. Numerical examples show that after simplification of the model, the computational efficiency of the time-delay system is greatly improved under the premise of ensuring the computational accuracy. (4) A new LMI criterion for time-delay stability is proposed, which is suitable for multi-time-delay systems and has higher solving efficiency: first of all, a new time-delay stability criterion is proposed for multi-time-delay systems. By constructing a new Lyapunov-Krasovskii functional and directly obtaining the condition that the derivative of the function is maximized by variational method, a new LMI criterion is formed, in which any free right matrix is avoided. It effectively reduces the number of variables to be found in the criterion. Furthermore, it is proved theoretically that the extremum condition of the new criterion is equivalent to the optimal value of the existing free-right matrix criterion. Finally, a typical second-order time-delay system, a single-machine-infinite bus system and a WSCC- 3 machine 9-bus system are used to verify the effectiveness of the proposed method. The calculation results show that the new criterion can solve the same time-delay stability margin with the same time-delay. The computational efficiency has been greatly improved.
【学位授予单位】：天津大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TM712
，
本文编号：2452260
[Abstract]:With the continuous expansion of power grid scale and the continuous improvement of interconnection degree, the security and stability of power grid operation are facing more and more challenges, and the related problems have been highly concerned by the power industry and academia. In order to improve the security and stability of power system operation, the coordinated control of wide area measurement system (WAMS) is a possible choice in the future, but there is obvious time delay in the transmission of wide area measurement system information. It will have a negative effect on the stable operation of the power system and the design of the related controllers, which need to be considered scientifically. The main work of this paper is as follows: (1) on the basis of deducing the key link and equipment mathematical model of power system in detail, the stability of power system with time-delay is studied in this paper. By means of linearization technique, the steady state model needed for small disturbance stability analysis of time-delay power system is obtained for further study, including: typical second-order time-delay system model, single-machine-infinite bus system model, and so on. WSCC- 3 machine 9-bus system model and IEEE- 10 machine 39-bus system model. (2) an effective method to solve the stability region of large-scale time-delay and small disturbance in power system is proposed. Firstly, the parameter transformation technique is used to solve the stability region of power system with time-delay and small disturbance. The solution of the boundary of the stability region with large time-delay and small disturbance is transformed into the search, translation and inverse translation of the finite parameter space, which greatly reduces the solution of the boundary of the stability region. Furthermore, by using the four-point interpolation method, the boundary properties and composition of the small perturbation stability region are determined by perturbing the critical points on the boundary of the stability region. Last, The effectiveness of the proposed method is verified by using the typical second-order time-delay system and the WSCC- 3 machine 9-node time-delay system. (3) A simplified method for single time-delay power system model is proposed and the applicable linear matrix is derived. The new criterion of inequality (LMI): first of all, the linear model of power system with time-delay links is proposed. Extend to include input-output link state space expression; Furthermore, the extended model is simplified by using the dimensionality reduction method based on the state space expression, and the number of variables to be solved is reduced as much as possible on the basis of retaining the key dynamics of the system. Finally, based on the simplified model, a new and more efficient delay-stable LMI criterion is derived. The method is applied to WSCC- 3-machine 9-bus system with time-delay and 39-bus system with IEEE- 10 machine. The results of single-delay stability margin of two power systems are compared by using binary search algorithm. Numerical examples show that after simplification of the model, the computational efficiency of the time-delay system is greatly improved under the premise of ensuring the computational accuracy. (4) A new LMI criterion for time-delay stability is proposed, which is suitable for multi-time-delay systems and has higher solving efficiency: first of all, a new time-delay stability criterion is proposed for multi-time-delay systems. By constructing a new Lyapunov-Krasovskii functional and directly obtaining the condition that the derivative of the function is maximized by variational method, a new LMI criterion is formed, in which any free right matrix is avoided. It effectively reduces the number of variables to be found in the criterion. Furthermore, it is proved theoretically that the extremum condition of the new criterion is equivalent to the optimal value of the existing free-right matrix criterion. Finally, a typical second-order time-delay system, a single-machine-infinite bus system and a WSCC- 3 machine 9-bus system are used to verify the effectiveness of the proposed method. The calculation results show that the new criterion can solve the same time-delay stability margin with the same time-delay. The computational efficiency has been greatly improved.
【学位授予单位】：天津大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TM712
，
本文编号：2452260
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