电力系统低频振荡的分析和控制
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摘要
随着电网规模的不断扩大，电力系统的动态稳定性问题越来越突出，系统互联引发的区域低频振荡问题严重威胁到互联电力系统的安全稳定运行，有必要深入研究互联系统中低频振荡的诱发机理及影响因素，进而找到有效的抑制措施。
本文研究了理想对称多机系统中的振荡情况，研究表明系统的振荡情况可等效为一个两机系统和一个单机-无穷大系统的振荡。继而在典型的三机系统中，分析了系统结构、运行方式以及参数的改变对振荡频率的影响；在一定的参数条件下，系统的多个振荡频率可较接近。当系统电气量中某两个主导振荡模式的频率差较小且振荡幅值相当时，该电气量会出现频率较低的差频振荡，其振荡频率约为这两个振荡频率的差值；当频率差足够小时，将产生超低频振荡现象。
本文从多方面分析比较了电力系统低频振荡的正规形法和模态级数法这两种非线性模式分析法的有效性。定义了指标EI来分析正规形法二阶参与因子的有效性，并定性比较了正规形方法和模态级数法的参与因子。为了比较低频振荡分析方法所得近似解逼近时域仿真解的程度，定义了误差指标err，并引入近似算法的有效域概念。继而从有效域和不同非线性程度下的有效性两个方面，比较了模态级数法、正规形法和线性模式分析法的有效性。在正规形法原有指标的基础上定义了一非线性指标，并以振荡模式的实际响应与线性响应的差，定性分析了系统模式的非线性程度，验证了该非线性指标的有效性。
本文研究了阻尼低频振荡的电力系统稳定器PSS的配置问题。指出若某机组参与因子的相位在二、三象限，即使其参与因子数值较大，在该机组上配置PSS反而会恶化系统的阻尼，因此，转速参与因子相位对阻尼控制效果有较大影响。提出了配置PSS的综合参与指标，该指标同时考虑了PSS输入信号以及闭环控制两方面的影响，可兼顾系统的多种运行方式，比传统的参与因子配置法更合理更有效。
本文进一步探讨了电力系统稳定器PSS广域反馈信号的选择问题。提出了用来选择信号的留数指标，并用实际留数的幅值和相角验证了该留数指标的有效性，该指标只需利用状态矩阵的左右特征向量，非常简便。分析了系统运行方式改变对参与因子和留数的影响，分析表明发电机转速的留数与其参与因子的变化趋势相同，这为广域反馈信号的选择提供了参考。在4机2区系统中，比较了局部信号、区域内组合信号以及区域间组合信号作为反馈信号的有效性和鲁棒性。
With the growing scale and complexity of power system, the power system dynamic stability issue became a critical problem. The inter-area low frequency oscillations caused by the interconnection of weakly coupled power systems threaten the security and stability of the interconnected power systems badly. It is an urgent task to investigate the mechanism and influencing factors of the inter-area low frequency oscillations, and design effective measures to damp the inter-area oscillations.
When analyzing the oscillation phenomenon in certain ideal and uniform multi-machine system, it is indicated that the oscillation frequencies are equivalent to the frequencies of two separate systems, where one system is a simple system with two generators while the other is the single-machine infinite bus system. By the example of a typical 3-generator system, the influences of system structure, operating conditions and parameters on the low oscillation frequency are studied. System frequencies might be comparable under certain parameter conditions. When the frequency difference of two system oscillation modes is small and the amplitudes of these two modes in some electric variable are comparable, this electric variable will present differential frequency oscillation with relatively low frequency. Furthermore, if the frequency difference is small enough, the phenomena of ultra low frequency oscillation will result.
The validity of two non-linear analysis methods for low frequency oscillation in power systems, i.e. normal form method and modal series method, are analyzed and compared from many aspects in this dissertation. An index El is defined to analyze the validity of the second-order participation factors of normal form method. Then the second-order participation factors of normal form method are qualitatively compared with that of modal series method. To evaluate the solution precision of different low frequency oscillation analysis methods, an error index err describing the closeness between the analysis result and the nonlinear simulation result is defined. The concept of valid region is then derived, which refers to the region in parameter space satisfying certain error index. The validity of normal form method, modal series method and linear modal method is compared through valid regions and the validity under different system stress condition. Besides, a nonlinearity index for normal form method is defined based on its original counterpart. The rationality of proposed index is proofed through comparing the real response and linear response of system modes.
The most suitable location for power system stabilizer(PSS) to damp low frequency oscillations is investigated in this dissertation. When the phase of some generator's speed-participation factor is in the second or third quadrant, the damping can be worsened when this generator is equipped with PSS even if the generator has a large speed participation factor. So the phase of speed-participation factor has a prominent influence on the damping control. A composite participation index that takes into account both the input and control effect of PSS controllers is proposed to identify the best PSS location, which can compromise the requirements of multiple system operating conditions. Hence it is a more reasonable and effective method than the conventional participation factor method.
The wide area feedback signal of power system stabilizer(PSS) is also discussed in this dissertation. A residue index is proposed to select the feedback signal for damping controllers and its validity is verified by the value and phase of real residues. This residue index is very convenient for it just needs the left and right eigenvectors of characteristic matrix. Through analyzing the influence of system operating condition on participation factors and residues, it is indicated that the change direction of generator speed residue is just the same as its participation factor. This gives some clues to select the wide area feedback signal for damping controller. By the example of a typical 2-area 4-generator power system, the validity and robustness of local signal, inner-area composite signals, inter-area composite signals used as feedback signal is compared.
本文研究了理想对称多机系统中的振荡情况，研究表明系统的振荡情况可等效为一个两机系统和一个单机-无穷大系统的振荡。继而在典型的三机系统中，分析了系统结构、运行方式以及参数的改变对振荡频率的影响；在一定的参数条件下，系统的多个振荡频率可较接近。当系统电气量中某两个主导振荡模式的频率差较小且振荡幅值相当时，该电气量会出现频率较低的差频振荡，其振荡频率约为这两个振荡频率的差值；当频率差足够小时，将产生超低频振荡现象。
本文从多方面分析比较了电力系统低频振荡的正规形法和模态级数法这两种非线性模式分析法的有效性。定义了指标EI来分析正规形法二阶参与因子的有效性，并定性比较了正规形方法和模态级数法的参与因子。为了比较低频振荡分析方法所得近似解逼近时域仿真解的程度，定义了误差指标err，并引入近似算法的有效域概念。继而从有效域和不同非线性程度下的有效性两个方面，比较了模态级数法、正规形法和线性模式分析法的有效性。在正规形法原有指标的基础上定义了一非线性指标，并以振荡模式的实际响应与线性响应的差，定性分析了系统模式的非线性程度，验证了该非线性指标的有效性。
本文研究了阻尼低频振荡的电力系统稳定器PSS的配置问题。指出若某机组参与因子的相位在二、三象限，即使其参与因子数值较大，在该机组上配置PSS反而会恶化系统的阻尼，因此，转速参与因子相位对阻尼控制效果有较大影响。提出了配置PSS的综合参与指标，该指标同时考虑了PSS输入信号以及闭环控制两方面的影响，可兼顾系统的多种运行方式，比传统的参与因子配置法更合理更有效。
本文进一步探讨了电力系统稳定器PSS广域反馈信号的选择问题。提出了用来选择信号的留数指标，并用实际留数的幅值和相角验证了该留数指标的有效性，该指标只需利用状态矩阵的左右特征向量，非常简便。分析了系统运行方式改变对参与因子和留数的影响，分析表明发电机转速的留数与其参与因子的变化趋势相同，这为广域反馈信号的选择提供了参考。在4机2区系统中，比较了局部信号、区域内组合信号以及区域间组合信号作为反馈信号的有效性和鲁棒性。
With the growing scale and complexity of power system, the power system dynamic stability issue became a critical problem. The inter-area low frequency oscillations caused by the interconnection of weakly coupled power systems threaten the security and stability of the interconnected power systems badly. It is an urgent task to investigate the mechanism and influencing factors of the inter-area low frequency oscillations, and design effective measures to damp the inter-area oscillations.
When analyzing the oscillation phenomenon in certain ideal and uniform multi-machine system, it is indicated that the oscillation frequencies are equivalent to the frequencies of two separate systems, where one system is a simple system with two generators while the other is the single-machine infinite bus system. By the example of a typical 3-generator system, the influences of system structure, operating conditions and parameters on the low oscillation frequency are studied. System frequencies might be comparable under certain parameter conditions. When the frequency difference of two system oscillation modes is small and the amplitudes of these two modes in some electric variable are comparable, this electric variable will present differential frequency oscillation with relatively low frequency. Furthermore, if the frequency difference is small enough, the phenomena of ultra low frequency oscillation will result.
The validity of two non-linear analysis methods for low frequency oscillation in power systems, i.e. normal form method and modal series method, are analyzed and compared from many aspects in this dissertation. An index El is defined to analyze the validity of the second-order participation factors of normal form method. Then the second-order participation factors of normal form method are qualitatively compared with that of modal series method. To evaluate the solution precision of different low frequency oscillation analysis methods, an error index err describing the closeness between the analysis result and the nonlinear simulation result is defined. The concept of valid region is then derived, which refers to the region in parameter space satisfying certain error index. The validity of normal form method, modal series method and linear modal method is compared through valid regions and the validity under different system stress condition. Besides, a nonlinearity index for normal form method is defined based on its original counterpart. The rationality of proposed index is proofed through comparing the real response and linear response of system modes.
The most suitable location for power system stabilizer(PSS) to damp low frequency oscillations is investigated in this dissertation. When the phase of some generator's speed-participation factor is in the second or third quadrant, the damping can be worsened when this generator is equipped with PSS even if the generator has a large speed participation factor. So the phase of speed-participation factor has a prominent influence on the damping control. A composite participation index that takes into account both the input and control effect of PSS controllers is proposed to identify the best PSS location, which can compromise the requirements of multiple system operating conditions. Hence it is a more reasonable and effective method than the conventional participation factor method.
The wide area feedback signal of power system stabilizer(PSS) is also discussed in this dissertation. A residue index is proposed to select the feedback signal for damping controllers and its validity is verified by the value and phase of real residues. This residue index is very convenient for it just needs the left and right eigenvectors of characteristic matrix. Through analyzing the influence of system operating condition on participation factors and residues, it is indicated that the change direction of generator speed residue is just the same as its participation factor. This gives some clues to select the wide area feedback signal for damping controller. By the example of a typical 2-area 4-generator power system, the validity and robustness of local signal, inner-area composite signals, inter-area composite signals used as feedback signal is compared.
引文
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