| 引用本文: | 赵洪山,薛 宁,时 宁.非线性电力系统模型经验Gramian平衡降阶[J].电力自动化设备,2014,34(9): |
| ZHAO Hongshan,XUE Ning,SHI Ning.Empirical Gramian balanced reduction of nonlinear power system model[J].Electric Power Automation Equipment,2014,34(9): |
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| 摘要: |
| 为解决多机非线性动态电力系统模型应用中存在的计算复杂、维数高的问题，提出经验Gramian平衡降阶方法，即将高阶非线性电力系统动态模型投影到一个低维子空间以获得其降阶模型，且降阶模型能够保留原非线性系统输入输出动态行为。其实现过程：形成非线性电力系统动态模型，通过仿真样本和经验数据样本得到经验可控Gramian矩阵和经验可观Gramian矩阵；利用得到的Gramian矩阵，计算平衡变换矩阵T，从而得到原系统的平衡系统；获得平衡系统的经验可控Gramian矩阵和经验可观Gramian矩阵，并进行奇异值分解，得到Hankel奇异值；根据Hankel奇异值大小的分布确定低维子空间的维数，得到非线性电力系统的降阶模型。以某实际20机非线性电力系统模型为例进行降阶仿真，仿真结果表明，降阶系统模型在保留原系统稳定性和输入输出动态行为的前提下，其阶数由原系统的120阶降到50阶，验证了经验Gramian平衡降阶方法在非线性电力系统模型降阶中的有效性。 |
| 关键词: 电力系统 非线性系统 模型 经验Gramian平衡降阶 模型降阶 奇异值分解 仿真 |
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| 基金项目:国家自然科学基金资助项目（51077053，51277074） |
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| Empirical Gramian balanced reduction of nonlinear power system model |
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ZHAO Hongshan, XUE Ning, SHI Ning
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State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources，
North China Electric Power University，Baoding 071003，China
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| Abstract: |
| The empirical Gramian balanced reduction method is proposed to reduce the dimensionality and complexity of nonlinear multi-machine power system model，which projects the high-dimensional nonlinear dynamic model to a low-dimensional subspace to obtain a reduced model while retains the original dynamic behaviors of its inputs and outputs. Its implementation is as followings：build the nonlinear dynamic model of power system；obtain the empirical controllable and observable Gramian matrices based on the simulative samples and experiential samples；calculate the transformation matrix T based on the obtained Gramian matrices to get the balanced model of original system and its empirical controllable and observable Gramian matrices；decomposite the singular values of obtained Gramian matrices of the balanced model to get the Hankel singular values；determine the subspace dimension according to the obtained Hankel singular values to get the reduced model. Simulation is carried out for an actual 20-generator nonlinear power system as an example and the simulative results show its dimension is reduced from 120 to 50 while its stability and the dynamic behaviors of its inputs and outputs are kept，verifying the effectiveness of the empirical Gramian balanced reduction method applied in the reduction of nonlinear power system model. |
| Key words: electric power systems nonlinear systems models empirical Gramian balanced reduction model reduction singular value decomposition computer simulation |
