大规模电力系统低频振荡分析与广域自适应控制研究
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摘要
随着“西电东送”战略的实施,我国电网通过一系列的联网工程形成了两大长链式同步交流电网。近年来,我国国家电网公司提出了建设“以特高压电网为骨干网架、各级电网协调发展”的战略目标。2009年1月6日,中国自主研发、设计和建设的1000kV晋东南—南阳—荆门特高压交流试验示范工程正式建成投运。根据规划,到“十二五”初期,我国将建成“两纵两横”特高压骨干电网,从而形成超大规模的华北—华中—华东特高压交流同步电网。到2020年前后,国家电网特高压网架将形成以华北、华中、华东为核心,联结各大区域电网、大煤电基地、大水电基地和主要负荷中心的坚强电网结构。
在我国特高压电网建设过程中,高低压电磁环网和重载的长距离特高压送电通道,都可能导致电网发生低频功率振荡。大规模电力系统规模巨大且运行方式多变,对现有的低频振荡分析和控制方法都提出了挑战。因此,开展大规模电力系统低频振荡分析和广域自适应控制,解决现有分析和控制方法在大规模电力系统应用中存在的不足,对于丰富和拓展电力系统低频振荡的分析和控制理论,防止大停电事故和提高区域电网间的输电能力都具有重要的理论意义和应用价值。在广泛阅读小干扰功角稳定机理、分析和控制方法方面相关文献的基础上,论文在大规模电力系统低频振荡的分析和广域自适应控制方面,进行了深入的研究和有益的探讨。论文的主要研究工作和创新性成果如下:
1)针对传统特征值分析方法仅适用于中小规模电力系统的局限性,结合Prony和稀疏特征值算法,提出了一种大规模互联电网区间低频振荡分析的实用方法。稀疏特征值分析方法,充分利用大规模电力系统小干扰稳定性分析中所形成的增广状态矩阵稀疏性的特点,能够计算系统全部特征值中我们所关心的特征子集,可分析任意规模的电力系统。利用Prony分析的结果作为稀疏特征值算法的初始位移点,从而可以快速、准确地计算出所关心的部分特征值和特征向量,避免了初始参数选取不当对稀疏特征值算法计算速度和收敛性能的不利影响。利用提出的方法,以逆迭代转Rayleigh商迭代和隐式重启动Arnoldi两种稀疏特征值算法为例,分别对东北—华北互联电力系统和华北—华中—华东特高压同步电网进行了低频振荡分析,得到了关键的区间低频振荡模式,在东北—华北互联电力系统配置了PSS以提高系统的阻尼,对华北—华中—华东特高压同步电网区间低频振荡模式的影响因素进行了深入分析。
东北—华北互联电力系统的低频振荡分析结果表明:系统存在山东电网机组相对于东北电网机组的弱阻尼区间低频振荡模式。对华北—华中—华东特高压同步电网进行低频振荡分析后,得到以下结论:系统主要存在六个区间低频振荡模式。山东电网机组相对于蒙西电网机组的振荡模式的阻尼随着华北主网向山东电网输送功率的增加而增强,并且在山东电网与华北主网之间的第二个联网工程(黄骅—滨州500kV双回线路)的投运而显著降低。在极端情况下,华北主网需要山东电网提供紧急功率支援时,该振荡模式的阻尼下降尤为严重。蒙西电网向华北主网输送功率的增加,有利于提高蒙西电网机组参与的区间低频振荡模式的阻尼。福建电网机组相对于系统的弱阻尼区间低频振荡模式的阻尼,随着福建电网向华东主网输送功率的增加而增强,且该模式的阻尼在杭北变电站失去所有的特高压线路后得到显著增加。安徽、浙江电网机组相对于江苏电网和阳城厂机组的振荡模式的阻尼,在杭北变电站失去所有的特高压线路后急剧减弱。石家庄特高压变电站的失去与否对系统区间低频振荡模式的阻尼影响很小。
2)在电力系统阻尼控制研究中,系统模型是进行控制器设计的前提和基础。针对现代互联电力系统规模巨大和运行方式复杂多变的特点,首次提出了阻尼控制中的在线递推闭环子空间辨识算法,着眼于解决“现辩现控”思想中的“辩”。在闭环情况下,利用由系统“过去的”输入和输出Hankel矩阵形成的辅助变量消除系统的输入输出测量噪声和过程噪声,并通过矩阵正交投影得到系统扩展可观性矩阵的列张成的子空间。借助奇异值分解和扩展可观性矩阵的转移不变特性得到系统矩阵A和C的实现,进而由最小二乘计算系统矩阵B和D。在新的采样数据到来时,利用扩展辅助变量投影估计子空间跟踪算法递推更新A和C,并由递推最小二乘算法更新B和D。论文还从系统模型的闭环可辨识性、持续激励信号的选择以及采样数据的尺度变换方面,对在线递推闭环子空间辨识算法应用于电力系统阻尼控制时应注意的问题,进行了探讨。在基于自校正原理的广域自适应阻尼控制系统结构下,利用在线递推闭环子空间辨识算法,设计了线性二次最优部分输出反馈的广域附加阻尼控制器。
利用电网的动态响应来辨识包含主导低频振荡模式的降阶模型,避开了实际系统模型阶次很高且不易获得的难题。在线递推闭环子空间辨识算法具有较好的数值稳定性和较低的时间复杂度,为实现“现辩现控”思想中的“控”打下基础。
中国电科院8机36节点系统的仿真结果表明,所提出的在线递推闭环子空间模型辨识算法,能够有效地辨识和跟踪包含系统的主导低频振荡模式的状态空间模型,并实现附加阻尼控制器参数的在线调整。基于广域信息的附加阻尼控制器能有效地抑制系统的区间低频振荡。
3)针对最优控制不能在优化求解过程中考虑控制约束的不足,提出了基于模型预测理论的广域阻尼控制策略,用以实现“现辩现控”思想中的“控”。在辨识得到的系统模型的基础上,用输出扰动对系统状态进行增广,得到系统的输出扰动模型,以防止系统输出产生静态偏差。通过Kalman滤波器得到输出扰动模型状态的估计值。在利用辨识模型得到闭环形式的预测方程后,分别建立表征在无限时域内系统响应偏离参考轨迹的代价和施加阻尼控制的代价的目标函数。考虑到控制输入的约束,最优控制量通过求解以当前系统状态为初始状态的最优控制问题得到。在线模型辨识和控制量的优化求解在有限时间间隔内反复进行。该控制策略是在线模型辨识和控制器参数在线更新的有机结合,实现了电力系统低频振荡的自适应控制,因此克服了基于离线辨识设计的固定参数控制器的固有缺点,解决了由于运行方式复杂多变和参数的不确定性与时变性引起的控制性能降低问题。采用模型预测、滚动优化和反馈校正策略可以预知系统在控制措施下的演化轨迹,避免了控制的负效应。
中国电科院8机36节点系统仿真结果表明,系统状态空间模型和模型预测控制律更新的最大耗时小于采样时间间隔,控制器能够满足在线应用的要求。控制器可以有效地抑制系统的区间低频振荡模式,并且具有与PSS和其他模型预测阻尼控制器相互协调和适应系统运行方式变化的能力。
With implementation of the "transmission of electricity from the western to the eastern region" strategy, two big and long-chain AC synchronized power grids have been formed in our country according to a series of interconnection projects. Recently, "ultra- high-voltage (UHV) grid as the backbone grid, coordinated development of power grids at all levels" strategical objective has been proposed by State Grid Corporation of China (SGCC). On January 6, 2009, the lOOOkV Jindongnan-Nanyang-Jingmen UHV AC experimental pilot project, which is researched, developed, designed and constructed independently by China, has been formally completed and put into operation. According to planning, "two vertical two horizontal" UHV backbone grid will be constructed and an ultra-large-scale North China-Central China-East China UHV AC synchronized power grid will be formed by the beginning of the "Twelfth Five-Year". By the year around 2020, a strong structure will be formed for UHV power grid of SGCC, which takes the North China, Central China and East China as the core, and links major regional power grids, large coal bases and large hydropower bases and main load centers.
During construction of our country's ultra-high voltage (UHV) power grid, both electromagnetic loop circuit and stressed long UHV transmission passage may lead to low frequency power oscillation. Large scale power system has a characteristic of large scale and variable operation condition. Both of them challenge existing low frequency analysis and control methods. Therefore, studies on low frequency analysis and wide-area adaptive control for large power system, which is used to overcome shortcomings of existing analysis and control methods in practical applications, has a great importance in enrichment and extension of power system low frequency oscillation analysis and control theory, prevention blackout and improvement transmission capacity between regional power systems. Based on literature review of studies on mechanism, analysis and control method on small disturbance angle stability, thorough studies and useful discussions on low frequency analysis method and wide-area adaptive control strategies for large power system have been made in this dissertation. The main research work and innovative fruits are as follows.
1) With regards to limitation of conventional eigenvalue analysis method holds true only for middle or small scale power system, a practical method for large scale interconnected power system low frequency oscillation analysis is proposed by combing Prony algorithm and sparse eigenvalue technique. Sparse eigenvalue analysis technique, which makes full use of sparsity of augmented state matrix during small disturbance stability analysis for large scale power system, can compute out concerned eigenvalue subset from all eigenvalues and can analysis power systems that have arbitrary scales. Those concerned partial eigenvalues and eigenvectors can be computed out quickly and accurately by taking results of Prony analysis as initial shift points for the algorithms. Thus adverse effects on computation speed and convergence performance for sparse eigenvalue technique due to inappropriate choice of initial parameters will be avoided. Based on the proposed method, two sparse eigenvalue algorithms, i.e., inverse iteration to Rayleigh quotient iteration (II/RQI) and implicitly restarted Arnoldi (IRA) are taken as examples to conduct low frequency oscillation analysis forNortheast China-North China interconnected power system and North China-Central China-East China UHV synchronized power grid. Critical interarea low frequency oscillation modes are obtained and power system stabilizers (PSSs) are installed on generators in Northeast China- North China interconnected power system to improve system damping. Influencing factors on interarea low frequency oscillation modes for North China-Central China- East China UHV synchronized power grid are also thoroughly analyzed.
Low frequency oscillation analysis results for Northeast China- North China interconnected power system show that there is a weak damping interarea low frequency oscillation mode where generators in Shandong power grid swing against those in Northeast China power grid. After low frequency oscillation analysis for North China-Central China-East China UHV synchronized power grid, following conclusion is drawn. There are six main interarea low frequency oscillation modes in the system. Damping ratio of the oscillation mode where generators in Shandong power grid swing against generators in Western Inner Mongolia power grid increases along with increment of power transmited from North China main grid to Shandong power grid. It declines sharply after the second interconnection project between North China main grid and Shandong power grid, Huanghua-Binzhou 500kV double-circuit transmission line, is put into operation. Extremely, when North China main grid needs emergency power from Shandong power grid, damping decline of this mode becomes more serious. Increment of power transmited from Western Inner Mongolia power grid to North China main grid helps enhance damping of modes in which generators in Western Inner Mongolia power grid participate. Damping ratio of mode where generators in Fujian power grid swing against generators in East China main grid increases along with increment of power transmited from Fujian power grid to East China main grid. Damping of this mode is notably enhanced after all UHV transmission lines in Hangbei substation are lost, while damping of oscillation mode where generators in Anhui and Zhejiang power grid swing against generators in Jiangsu power grid and Yangcheng power plant declines sharply after the lost. Whether Shijiazhuang UHV substation is lost or not, has little impact on all interarea low frequency oscillation modes.
2) In power system damping control research, system model is premise and basis for controller design. With respect to modern interconnected power system, which has a characteristic of large scale and variable and complex operation conditions, online recursive closed-loop subspace identification algorithm, i.e., past output errors in variables-multivariable output error state space model identification algorithm (POEIV-MOESP), is proposed. It is the first time that this algorithm is proposed for damping control. The algorithm mainly focus on solving "identification" in "control while identification" thought. Under closed-loop condition, system input and output measurement noises as well as process noise are eliminated by instrumental variable which is formed by system "past" input and output Hankel matrices. Then, space spanned by the columns of system extended observability matrix is obtained by matrix orthogonal projection. With the help of singular value decomposition (SVD) and shift invariant characteristic of extended observability matrix, system matrices A and C can be derived. Thereafter, matrices B and D can be computed out by using least square algorithm. When new sampled input and output data become available, extended instrumental variable- projection approximate subspace tracking algorithm (EIV-PAST) is used to recursively update A and C, while recursive least square (RLS) algorithm is utilized to recursively update B and D. Aspects on applying the algorithm to power system damping control, such as closed-loop identifiability of system model, choice of persistent excitation signal and scaling factor for sampled data, are also discussed in this dissertation. Under the self-tuning principle based wide-area adaptive damping control framework, linear quadratic optimal partial output feedback supplementary damping controller is designed by using online recursive closed-loop subspace identification algorithm.
The algorithm use system dynamic response to identify reduced-order model which contains system dominant low frequency oscillation modes. Thus, difficulty in obtaining practical system model which has very high order is avoided. Additionally, the algorithm has good numerical stability and low time complexity, which provides basis for "control" in "control while identification" thought.
Simulation results of the China EPRI 8-machine 36-bus system demonstrate that the proposed on-line recursive closed-loop identification algorithm can effectively identify and track reduced- order state space model which contains system dominant low frequency oscillation modes, and can be used to adjust parameters of supplementary damping controller on-line. Additionally, supplementary damping controller can effectively damp system intearea low frequency oscillations.
3) With regards to shortcoming of optimal control which cannot take control constraints into the optimization, wide-area adaptive damping control strategy based on model predictive control (MPC) is proposed, which attempts to solving "control" in "control while identification" thought. Based on identified model, system output disturbance model is obtained by augmenting system states with output disturbances to prevent outputs from steady-state offsets. Kalman filter is used to estimate states the augmented model. According to the identified model, predictive equations for closed-loop system are formulated. Then an objective function representing the cost of deviation of system responses from the reference trajectory and the cost of imposing damping controls in infinite horizon is established. Considering constraints on control input, optimal control can be obtained by solving this optimal control problem which uses current state of power system as the initial state. Online model identification and control optimization are repeated in each time interval. The proposed method is an organic integration of online model identification and online updating control parameters. It accomplishes adaptive control of power system low frequency oscillation. Thus, the inherent shortcomings of controllers with fixed parameters based on offline identification are overcome and the problem of the control performance degradation due to variation of the complex operation conditions and time-varying and uncertain characteristic of system parameters are solved. Negative effects of control are avoided by adopting model prediction, receding optimization and feedback compensation strategy in this method.
Simulation results of the China EPRI 8-machine 36-bus system demonstrate that time consumption for updating of system state space model and model predictive control law is less than sampling interval. Thus, model predictive damping controllers satisfy requirements for online application. It can effectively damp inter-area low frequency oscillation modes. It also have the ability to coordinate with PSSs and other model predictive damping controllers in multi-machine power systems and the ability to adapt to changes in operation conditions.
在我国特高压电网建设过程中,高低压电磁环网和重载的长距离特高压送电通道,都可能导致电网发生低频功率振荡。大规模电力系统规模巨大且运行方式多变,对现有的低频振荡分析和控制方法都提出了挑战。因此,开展大规模电力系统低频振荡分析和广域自适应控制,解决现有分析和控制方法在大规模电力系统应用中存在的不足,对于丰富和拓展电力系统低频振荡的分析和控制理论,防止大停电事故和提高区域电网间的输电能力都具有重要的理论意义和应用价值。在广泛阅读小干扰功角稳定机理、分析和控制方法方面相关文献的基础上,论文在大规模电力系统低频振荡的分析和广域自适应控制方面,进行了深入的研究和有益的探讨。论文的主要研究工作和创新性成果如下:
1)针对传统特征值分析方法仅适用于中小规模电力系统的局限性,结合Prony和稀疏特征值算法,提出了一种大规模互联电网区间低频振荡分析的实用方法。稀疏特征值分析方法,充分利用大规模电力系统小干扰稳定性分析中所形成的增广状态矩阵稀疏性的特点,能够计算系统全部特征值中我们所关心的特征子集,可分析任意规模的电力系统。利用Prony分析的结果作为稀疏特征值算法的初始位移点,从而可以快速、准确地计算出所关心的部分特征值和特征向量,避免了初始参数选取不当对稀疏特征值算法计算速度和收敛性能的不利影响。利用提出的方法,以逆迭代转Rayleigh商迭代和隐式重启动Arnoldi两种稀疏特征值算法为例,分别对东北—华北互联电力系统和华北—华中—华东特高压同步电网进行了低频振荡分析,得到了关键的区间低频振荡模式,在东北—华北互联电力系统配置了PSS以提高系统的阻尼,对华北—华中—华东特高压同步电网区间低频振荡模式的影响因素进行了深入分析。
东北—华北互联电力系统的低频振荡分析结果表明:系统存在山东电网机组相对于东北电网机组的弱阻尼区间低频振荡模式。对华北—华中—华东特高压同步电网进行低频振荡分析后,得到以下结论:系统主要存在六个区间低频振荡模式。山东电网机组相对于蒙西电网机组的振荡模式的阻尼随着华北主网向山东电网输送功率的增加而增强,并且在山东电网与华北主网之间的第二个联网工程(黄骅—滨州500kV双回线路)的投运而显著降低。在极端情况下,华北主网需要山东电网提供紧急功率支援时,该振荡模式的阻尼下降尤为严重。蒙西电网向华北主网输送功率的增加,有利于提高蒙西电网机组参与的区间低频振荡模式的阻尼。福建电网机组相对于系统的弱阻尼区间低频振荡模式的阻尼,随着福建电网向华东主网输送功率的增加而增强,且该模式的阻尼在杭北变电站失去所有的特高压线路后得到显著增加。安徽、浙江电网机组相对于江苏电网和阳城厂机组的振荡模式的阻尼,在杭北变电站失去所有的特高压线路后急剧减弱。石家庄特高压变电站的失去与否对系统区间低频振荡模式的阻尼影响很小。
2)在电力系统阻尼控制研究中,系统模型是进行控制器设计的前提和基础。针对现代互联电力系统规模巨大和运行方式复杂多变的特点,首次提出了阻尼控制中的在线递推闭环子空间辨识算法,着眼于解决“现辩现控”思想中的“辩”。在闭环情况下,利用由系统“过去的”输入和输出Hankel矩阵形成的辅助变量消除系统的输入输出测量噪声和过程噪声,并通过矩阵正交投影得到系统扩展可观性矩阵的列张成的子空间。借助奇异值分解和扩展可观性矩阵的转移不变特性得到系统矩阵A和C的实现,进而由最小二乘计算系统矩阵B和D。在新的采样数据到来时,利用扩展辅助变量投影估计子空间跟踪算法递推更新A和C,并由递推最小二乘算法更新B和D。论文还从系统模型的闭环可辨识性、持续激励信号的选择以及采样数据的尺度变换方面,对在线递推闭环子空间辨识算法应用于电力系统阻尼控制时应注意的问题,进行了探讨。在基于自校正原理的广域自适应阻尼控制系统结构下,利用在线递推闭环子空间辨识算法,设计了线性二次最优部分输出反馈的广域附加阻尼控制器。
利用电网的动态响应来辨识包含主导低频振荡模式的降阶模型,避开了实际系统模型阶次很高且不易获得的难题。在线递推闭环子空间辨识算法具有较好的数值稳定性和较低的时间复杂度,为实现“现辩现控”思想中的“控”打下基础。
中国电科院8机36节点系统的仿真结果表明,所提出的在线递推闭环子空间模型辨识算法,能够有效地辨识和跟踪包含系统的主导低频振荡模式的状态空间模型,并实现附加阻尼控制器参数的在线调整。基于广域信息的附加阻尼控制器能有效地抑制系统的区间低频振荡。
3)针对最优控制不能在优化求解过程中考虑控制约束的不足,提出了基于模型预测理论的广域阻尼控制策略,用以实现“现辩现控”思想中的“控”。在辨识得到的系统模型的基础上,用输出扰动对系统状态进行增广,得到系统的输出扰动模型,以防止系统输出产生静态偏差。通过Kalman滤波器得到输出扰动模型状态的估计值。在利用辨识模型得到闭环形式的预测方程后,分别建立表征在无限时域内系统响应偏离参考轨迹的代价和施加阻尼控制的代价的目标函数。考虑到控制输入的约束,最优控制量通过求解以当前系统状态为初始状态的最优控制问题得到。在线模型辨识和控制量的优化求解在有限时间间隔内反复进行。该控制策略是在线模型辨识和控制器参数在线更新的有机结合,实现了电力系统低频振荡的自适应控制,因此克服了基于离线辨识设计的固定参数控制器的固有缺点,解决了由于运行方式复杂多变和参数的不确定性与时变性引起的控制性能降低问题。采用模型预测、滚动优化和反馈校正策略可以预知系统在控制措施下的演化轨迹,避免了控制的负效应。
中国电科院8机36节点系统仿真结果表明,系统状态空间模型和模型预测控制律更新的最大耗时小于采样时间间隔,控制器能够满足在线应用的要求。控制器可以有效地抑制系统的区间低频振荡模式,并且具有与PSS和其他模型预测阻尼控制器相互协调和适应系统运行方式变化的能力。
With implementation of the "transmission of electricity from the western to the eastern region" strategy, two big and long-chain AC synchronized power grids have been formed in our country according to a series of interconnection projects. Recently, "ultra- high-voltage (UHV) grid as the backbone grid, coordinated development of power grids at all levels" strategical objective has been proposed by State Grid Corporation of China (SGCC). On January 6, 2009, the lOOOkV Jindongnan-Nanyang-Jingmen UHV AC experimental pilot project, which is researched, developed, designed and constructed independently by China, has been formally completed and put into operation. According to planning, "two vertical two horizontal" UHV backbone grid will be constructed and an ultra-large-scale North China-Central China-East China UHV AC synchronized power grid will be formed by the beginning of the "Twelfth Five-Year". By the year around 2020, a strong structure will be formed for UHV power grid of SGCC, which takes the North China, Central China and East China as the core, and links major regional power grids, large coal bases and large hydropower bases and main load centers.
During construction of our country's ultra-high voltage (UHV) power grid, both electromagnetic loop circuit and stressed long UHV transmission passage may lead to low frequency power oscillation. Large scale power system has a characteristic of large scale and variable operation condition. Both of them challenge existing low frequency analysis and control methods. Therefore, studies on low frequency analysis and wide-area adaptive control for large power system, which is used to overcome shortcomings of existing analysis and control methods in practical applications, has a great importance in enrichment and extension of power system low frequency oscillation analysis and control theory, prevention blackout and improvement transmission capacity between regional power systems. Based on literature review of studies on mechanism, analysis and control method on small disturbance angle stability, thorough studies and useful discussions on low frequency analysis method and wide-area adaptive control strategies for large power system have been made in this dissertation. The main research work and innovative fruits are as follows.
1) With regards to limitation of conventional eigenvalue analysis method holds true only for middle or small scale power system, a practical method for large scale interconnected power system low frequency oscillation analysis is proposed by combing Prony algorithm and sparse eigenvalue technique. Sparse eigenvalue analysis technique, which makes full use of sparsity of augmented state matrix during small disturbance stability analysis for large scale power system, can compute out concerned eigenvalue subset from all eigenvalues and can analysis power systems that have arbitrary scales. Those concerned partial eigenvalues and eigenvectors can be computed out quickly and accurately by taking results of Prony analysis as initial shift points for the algorithms. Thus adverse effects on computation speed and convergence performance for sparse eigenvalue technique due to inappropriate choice of initial parameters will be avoided. Based on the proposed method, two sparse eigenvalue algorithms, i.e., inverse iteration to Rayleigh quotient iteration (II/RQI) and implicitly restarted Arnoldi (IRA) are taken as examples to conduct low frequency oscillation analysis forNortheast China-North China interconnected power system and North China-Central China-East China UHV synchronized power grid. Critical interarea low frequency oscillation modes are obtained and power system stabilizers (PSSs) are installed on generators in Northeast China- North China interconnected power system to improve system damping. Influencing factors on interarea low frequency oscillation modes for North China-Central China- East China UHV synchronized power grid are also thoroughly analyzed.
Low frequency oscillation analysis results for Northeast China- North China interconnected power system show that there is a weak damping interarea low frequency oscillation mode where generators in Shandong power grid swing against those in Northeast China power grid. After low frequency oscillation analysis for North China-Central China-East China UHV synchronized power grid, following conclusion is drawn. There are six main interarea low frequency oscillation modes in the system. Damping ratio of the oscillation mode where generators in Shandong power grid swing against generators in Western Inner Mongolia power grid increases along with increment of power transmited from North China main grid to Shandong power grid. It declines sharply after the second interconnection project between North China main grid and Shandong power grid, Huanghua-Binzhou 500kV double-circuit transmission line, is put into operation. Extremely, when North China main grid needs emergency power from Shandong power grid, damping decline of this mode becomes more serious. Increment of power transmited from Western Inner Mongolia power grid to North China main grid helps enhance damping of modes in which generators in Western Inner Mongolia power grid participate. Damping ratio of mode where generators in Fujian power grid swing against generators in East China main grid increases along with increment of power transmited from Fujian power grid to East China main grid. Damping of this mode is notably enhanced after all UHV transmission lines in Hangbei substation are lost, while damping of oscillation mode where generators in Anhui and Zhejiang power grid swing against generators in Jiangsu power grid and Yangcheng power plant declines sharply after the lost. Whether Shijiazhuang UHV substation is lost or not, has little impact on all interarea low frequency oscillation modes.
2) In power system damping control research, system model is premise and basis for controller design. With respect to modern interconnected power system, which has a characteristic of large scale and variable and complex operation conditions, online recursive closed-loop subspace identification algorithm, i.e., past output errors in variables-multivariable output error state space model identification algorithm (POEIV-MOESP), is proposed. It is the first time that this algorithm is proposed for damping control. The algorithm mainly focus on solving "identification" in "control while identification" thought. Under closed-loop condition, system input and output measurement noises as well as process noise are eliminated by instrumental variable which is formed by system "past" input and output Hankel matrices. Then, space spanned by the columns of system extended observability matrix is obtained by matrix orthogonal projection. With the help of singular value decomposition (SVD) and shift invariant characteristic of extended observability matrix, system matrices A and C can be derived. Thereafter, matrices B and D can be computed out by using least square algorithm. When new sampled input and output data become available, extended instrumental variable- projection approximate subspace tracking algorithm (EIV-PAST) is used to recursively update A and C, while recursive least square (RLS) algorithm is utilized to recursively update B and D. Aspects on applying the algorithm to power system damping control, such as closed-loop identifiability of system model, choice of persistent excitation signal and scaling factor for sampled data, are also discussed in this dissertation. Under the self-tuning principle based wide-area adaptive damping control framework, linear quadratic optimal partial output feedback supplementary damping controller is designed by using online recursive closed-loop subspace identification algorithm.
The algorithm use system dynamic response to identify reduced-order model which contains system dominant low frequency oscillation modes. Thus, difficulty in obtaining practical system model which has very high order is avoided. Additionally, the algorithm has good numerical stability and low time complexity, which provides basis for "control" in "control while identification" thought.
Simulation results of the China EPRI 8-machine 36-bus system demonstrate that the proposed on-line recursive closed-loop identification algorithm can effectively identify and track reduced- order state space model which contains system dominant low frequency oscillation modes, and can be used to adjust parameters of supplementary damping controller on-line. Additionally, supplementary damping controller can effectively damp system intearea low frequency oscillations.
3) With regards to shortcoming of optimal control which cannot take control constraints into the optimization, wide-area adaptive damping control strategy based on model predictive control (MPC) is proposed, which attempts to solving "control" in "control while identification" thought. Based on identified model, system output disturbance model is obtained by augmenting system states with output disturbances to prevent outputs from steady-state offsets. Kalman filter is used to estimate states the augmented model. According to the identified model, predictive equations for closed-loop system are formulated. Then an objective function representing the cost of deviation of system responses from the reference trajectory and the cost of imposing damping controls in infinite horizon is established. Considering constraints on control input, optimal control can be obtained by solving this optimal control problem which uses current state of power system as the initial state. Online model identification and control optimization are repeated in each time interval. The proposed method is an organic integration of online model identification and online updating control parameters. It accomplishes adaptive control of power system low frequency oscillation. Thus, the inherent shortcomings of controllers with fixed parameters based on offline identification are overcome and the problem of the control performance degradation due to variation of the complex operation conditions and time-varying and uncertain characteristic of system parameters are solved. Negative effects of control are avoided by adopting model prediction, receding optimization and feedback compensation strategy in this method.
Simulation results of the China EPRI 8-machine 36-bus system demonstrate that time consumption for updating of system state space model and model predictive control law is less than sampling interval. Thus, model predictive damping controllers satisfy requirements for online application. It can effectively damp inter-area low frequency oscillation modes. It also have the ability to coordinate with PSSs and other model predictive damping controllers in multi-machine power systems and the ability to adapt to changes in operation conditions.
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