基于SGEAC法的暂态稳定分析
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摘要
暂态稳定分析与控制一直是电力系统运行中最为严峻的问题之一。尽管在这方面已经进行了较为深入的研究,并且取得了丰硕的研究成果,但是分析方法大都或多或少建立在各自的假设下,当实际情况与这些假设不符时,可能造成非常大的分析误差或完全不同的结果。
本文从暂态稳定分析与控制工程应用实际的需要出发,在建立暂态稳定分析模型时没有引入任何近似与假设的情况下,围绕暂态稳定分析与控制的的准确性与快速性、适应性方面展开研究工作,并将稳定性理论应用到WAMS系统与电力市场分析中。
暂态稳定分析与控制的难点是必须做到快速性与准确性的统一。稳定分析的快速性是指能满足系统实时控制的需要,准确性是指付诸实施的控制措施应该满足经济性与可靠性的需要。二者必须高度统一。
为了做到快速性与准确性,本文以单机等面积定则原理(SGEAC)思想,将数值计算技术的普适性和解释方法的定量性结合起来,首先提出了一种具有隐式积分效果的显式积分方法,该方法以欧拉法为启动方式,通过对发电机节点或负荷节点进行处理,使雅可比矩阵定常,并将状态量或代数量收敛为每一步的积分终止判据,该方法结合了显式积分法与隐式积分法的特点,将迭代网络求解方法与本文提出的显式迭代方法结合起来,因此该方法具有显式积分法的速度,但其精度和数值稳定性与隐式积分法相同。实际大规模系统仿真表明,本文方法显著地改善了隐式积分法的速度,在程序设计上具有很好的可扩展性与灵活性。
其次本文以SGEAC思想为理论基石,定义了基于动态单等值机群的全局暂态稳定裕度。对基于动态单等值机群的稳定裕度与基于动态二等值机群(OMIB)相对运动的稳定裕度进行了比较研究。理论与实例分析证明了基于SGEAC思想的动态单机群稳定裕度与基于动态二机群相对运动的稳定裕度完全一致。与其它如EEAC、SIME等方法相比,SGEAC法可以考虑详尽的系统元件稳态与暂态模型,即具有时域仿真方法对元件模型的适应性；同时,本文方法不必进行失稳模式的判别,从而避免了因失稳模式的误判带来错误结果。因此,本文暂态稳定分析模型没有引入任何的近似与假设,从而确保了算法的准确性。
本文在保证算法模型的准确性的情况下,提出了功角曲线快速拟合的思想,进一步提高了暂态稳定分析的速度。通过理论分析,在COI坐标系下,单机等值机群的电磁功率可表示为功角多项式函数。根据单机等面积稳定判据原理,把发电机功角曲线展开成自变量为功角的高阶泰勒级数,采用时域仿真的办法对受扰系统进行短时间的仿真,根据少量仿真结果对机组电磁功率与转子相对功角曲线进行拟合。用得到的功角曲线预测机组的最大减速面积与加速面积,从而可以计算出系统的单摆和多摆的稳定裕度与不稳定裕度。该方法既具有时域仿真方法的精确性与良好的适应性,同时可得出基于加速面积与减速面积的能量型稳定裕度在此研究基础上,本文提出一种基于WAMS过程数据的快速暂态稳定预测评估方法,该方法利用发电机本地过程测量信息,采用滚动拟合预测方法,就能快速预测出系统的稳定裕度、临界机组及控制装置执行的时间裕度,通过对不同失步模式的实例验分析验证了所提方法的有效性,该方法在在线暂态稳定分析中应有广阔的应用前景。
除了判断系统稳定性外,另一个重要问题是假如系统将失去稳定,该如何施加适当的控制量以避免系统失稳或实现预定目标,这是本文研究的另一重要内容。它涉及电力系统稳定量化分析和稳定量化指标对控制变量的影响,即使在离线环境下这也是一个难点,实时环境下要求快速给出适当的控制量将更加困难。文章的最后在电力市场环境下的考虑暂态稳定约束的最大输电能力问题,以此提出基于SGEAC法如何给出控制量及调整策略的问题。该方法利用SGEAC法对预想事故快速扫描、找出严重故障,并计算出临界机组的功率转移量的估计值,进而提出发电计划调整策略。该方法不必进行失稳模式的判别,避免了穷尽式搜索,能够适应多重故障、多摆失稳场景和不同的失稳模式。同时,该算法对所有严重故障集同时处理,满足了实时预防控制的要求。通过对不同失步模式的实例分析验证了所提方法的有效性。同时,发电计划调整策略及方法还可用于预防控制。
Transient stability analysis and control is one of the most severe problems in power system operation. Although many efforts have been taken to study the problem and plentiful and substantial results have been achieved in many respects. However, most transient stability analytical methods more or less make the strong assumptions. When the reality does not match these assumptions, these may result in very large analytical error.
In this paper, the research work emphasis on the transient stability analysis and control in terms of accuracy, celerity and adaptability of different device model in the absence of any approximation or using hypothetical situations which meet transient stability analysis and control engineering application of the actual needs. Meanwhile, achievements in the research may be applied to WAMS.
The difficulty of transient stability analysis and control is that the result must be got rapidly and accurately. The rapidity implies that it is able to meet the needs of real-time control; accuracy referring to the implementation of control measures should meet the needs of the economy and reliability. Both must be highly uniform.
To meet the needs uniformly, the proposed transient stability analysis based on single generator equal area criterion (SGEAC) combines universality of the numerical integration method with quantity of the interpretation method in this paper. To improve the rapidity, this paper presents a new numerical integration method, which starts with Euler's method, and ends with the convergence of state or/and algebraic variables each step. Meanwhile, the Jacobian matrix comes to invariable by deal with the generators'nodes and loads'nodes in the computing process. So, it combines the fast speed of the explicit integration method with the accuracy of the implicit integration method for solving the network equation iteratively. Therefore, the compute speed corresponds with the explicit integration method, but its precision and the numeric stability are the same as the implicit integration method. The actual large-scale system simulation shows that this method significantly improves the speed of implicit integration method, and has a good scalability and flexibility in the program design.
Furthermore, the global transient stability margin based on dynamic single-equivalent machine is defined in the paper whose theoretical basis is on SGEAC. And it is compared with the stability margin based on the mutual motion of dynamic two groups of equivalent machine (OMIB). It is proved that single equivalent based stability margin is exactly identical with the stability margin based on one machine infinite bus (OMIB) equivalent in theory and nature. Compared with such methods as EEAC and SIME, detailed system model of steady state and transient can be considered in SGEAC. Therefore, it has the universality of the numerical integration method. Meanwhile, it is not necessary to identify the equivalent machines to avoid getting wrong stability evaluation. The accuracy of the algorithm is ensured without any assumptions or using hypothetical situations.
In the guarantee algorithm model's accurate situation, the power-angle curve fitting method is proposed to calculate the transient stability margin or the transient instability margin for further speeding transient stability analysis in this paper. The electromagnetic power of single equivalent is expressed by the polynomial function according to the proposed Taylor series expansion analysis in the COI frame by theoretical analysis. The curve between electric power of generator unit and rotor's angle in relative to center of inertia is expanded by Taylor's series based on single generation equivalent area criteria theory (SGEAC). By using SGEAC and combining with time domain simulation method, the disturbed system is simulated for a very short time period. According to the simulation result, the curve between electric power of generator unit and rotor's angle in relative to center of inertia is fitted. Maximum deceleration area or maximum acceleration area of each unit is obtained according to the fitted curves and then the stability margin and instability margin for the system are obtained. This method has advantage of good accuracy and adaptability of time-domain simulation method and by using the method, the energy type stability margin is obtained. A fast transient stability prediction method based on the WAMS process measurement is proposed in this paper. It can quickly predict the system stability margin, the moment when the system loses stability and control devices' response time by scrolling the measurement data which have been measured by the local PMU. Practical system analysis shows that the method is very efficient, and it should have wide engineering applications for on-line stability monitoring.
In addition to evaluate the stability of the system, another important issue is that if the system will lose stability, how to apply the appropriate amount of control to prevent system instability or to achieve the intended target, which is another important part of this paper. It involves quantitative analysis of power system stability and quantitative indicators' impact on control variables, even in the offline environment, this is a difficult, it will be more difficult in real-time environment that require fast given the appropriate amount of control. Fianally, a method is proposed for allocating generation so as to maximize power transfer between areas of interconnected systems under transient stability constraints. The proposed method is to specify how to give control or adjust strategy by SGEAC. This transient stability-constrained maximum allowable transfer method consists of screening a large number of contingencies, scrutinizing the dangerous ones, calculating the shifting active power generation of critical generators and suggesting generation rescheduling patterns to stabilize them by SGEAC. The method is accurate and adaptable as the time domain simulation method, but also stability margin based on single machine energy can be obtained. Compared with other energy function, it is not necessary to determine the correct two-group mode, can apply in multiply contingencies, multi-swing instability scenarios and different instability modes. It avoids exhaustive search. In addition, by controlling all dangerous contingencies simultaneously, the method succeeds in being fully compatible with requirements for real-time preventive monitoring and control. Lots of example analysis with different losing synchronism modes verified the proposed method.
本文从暂态稳定分析与控制工程应用实际的需要出发,在建立暂态稳定分析模型时没有引入任何近似与假设的情况下,围绕暂态稳定分析与控制的的准确性与快速性、适应性方面展开研究工作,并将稳定性理论应用到WAMS系统与电力市场分析中。
暂态稳定分析与控制的难点是必须做到快速性与准确性的统一。稳定分析的快速性是指能满足系统实时控制的需要,准确性是指付诸实施的控制措施应该满足经济性与可靠性的需要。二者必须高度统一。
为了做到快速性与准确性,本文以单机等面积定则原理(SGEAC)思想,将数值计算技术的普适性和解释方法的定量性结合起来,首先提出了一种具有隐式积分效果的显式积分方法,该方法以欧拉法为启动方式,通过对发电机节点或负荷节点进行处理,使雅可比矩阵定常,并将状态量或代数量收敛为每一步的积分终止判据,该方法结合了显式积分法与隐式积分法的特点,将迭代网络求解方法与本文提出的显式迭代方法结合起来,因此该方法具有显式积分法的速度,但其精度和数值稳定性与隐式积分法相同。实际大规模系统仿真表明,本文方法显著地改善了隐式积分法的速度,在程序设计上具有很好的可扩展性与灵活性。
其次本文以SGEAC思想为理论基石,定义了基于动态单等值机群的全局暂态稳定裕度。对基于动态单等值机群的稳定裕度与基于动态二等值机群(OMIB)相对运动的稳定裕度进行了比较研究。理论与实例分析证明了基于SGEAC思想的动态单机群稳定裕度与基于动态二机群相对运动的稳定裕度完全一致。与其它如EEAC、SIME等方法相比,SGEAC法可以考虑详尽的系统元件稳态与暂态模型,即具有时域仿真方法对元件模型的适应性；同时,本文方法不必进行失稳模式的判别,从而避免了因失稳模式的误判带来错误结果。因此,本文暂态稳定分析模型没有引入任何的近似与假设,从而确保了算法的准确性。
本文在保证算法模型的准确性的情况下,提出了功角曲线快速拟合的思想,进一步提高了暂态稳定分析的速度。通过理论分析,在COI坐标系下,单机等值机群的电磁功率可表示为功角多项式函数。根据单机等面积稳定判据原理,把发电机功角曲线展开成自变量为功角的高阶泰勒级数,采用时域仿真的办法对受扰系统进行短时间的仿真,根据少量仿真结果对机组电磁功率与转子相对功角曲线进行拟合。用得到的功角曲线预测机组的最大减速面积与加速面积,从而可以计算出系统的单摆和多摆的稳定裕度与不稳定裕度。该方法既具有时域仿真方法的精确性与良好的适应性,同时可得出基于加速面积与减速面积的能量型稳定裕度在此研究基础上,本文提出一种基于WAMS过程数据的快速暂态稳定预测评估方法,该方法利用发电机本地过程测量信息,采用滚动拟合预测方法,就能快速预测出系统的稳定裕度、临界机组及控制装置执行的时间裕度,通过对不同失步模式的实例验分析验证了所提方法的有效性,该方法在在线暂态稳定分析中应有广阔的应用前景。
除了判断系统稳定性外,另一个重要问题是假如系统将失去稳定,该如何施加适当的控制量以避免系统失稳或实现预定目标,这是本文研究的另一重要内容。它涉及电力系统稳定量化分析和稳定量化指标对控制变量的影响,即使在离线环境下这也是一个难点,实时环境下要求快速给出适当的控制量将更加困难。文章的最后在电力市场环境下的考虑暂态稳定约束的最大输电能力问题,以此提出基于SGEAC法如何给出控制量及调整策略的问题。该方法利用SGEAC法对预想事故快速扫描、找出严重故障,并计算出临界机组的功率转移量的估计值,进而提出发电计划调整策略。该方法不必进行失稳模式的判别,避免了穷尽式搜索,能够适应多重故障、多摆失稳场景和不同的失稳模式。同时,该算法对所有严重故障集同时处理,满足了实时预防控制的要求。通过对不同失步模式的实例分析验证了所提方法的有效性。同时,发电计划调整策略及方法还可用于预防控制。
Transient stability analysis and control is one of the most severe problems in power system operation. Although many efforts have been taken to study the problem and plentiful and substantial results have been achieved in many respects. However, most transient stability analytical methods more or less make the strong assumptions. When the reality does not match these assumptions, these may result in very large analytical error.
In this paper, the research work emphasis on the transient stability analysis and control in terms of accuracy, celerity and adaptability of different device model in the absence of any approximation or using hypothetical situations which meet transient stability analysis and control engineering application of the actual needs. Meanwhile, achievements in the research may be applied to WAMS.
The difficulty of transient stability analysis and control is that the result must be got rapidly and accurately. The rapidity implies that it is able to meet the needs of real-time control; accuracy referring to the implementation of control measures should meet the needs of the economy and reliability. Both must be highly uniform.
To meet the needs uniformly, the proposed transient stability analysis based on single generator equal area criterion (SGEAC) combines universality of the numerical integration method with quantity of the interpretation method in this paper. To improve the rapidity, this paper presents a new numerical integration method, which starts with Euler's method, and ends with the convergence of state or/and algebraic variables each step. Meanwhile, the Jacobian matrix comes to invariable by deal with the generators'nodes and loads'nodes in the computing process. So, it combines the fast speed of the explicit integration method with the accuracy of the implicit integration method for solving the network equation iteratively. Therefore, the compute speed corresponds with the explicit integration method, but its precision and the numeric stability are the same as the implicit integration method. The actual large-scale system simulation shows that this method significantly improves the speed of implicit integration method, and has a good scalability and flexibility in the program design.
Furthermore, the global transient stability margin based on dynamic single-equivalent machine is defined in the paper whose theoretical basis is on SGEAC. And it is compared with the stability margin based on the mutual motion of dynamic two groups of equivalent machine (OMIB). It is proved that single equivalent based stability margin is exactly identical with the stability margin based on one machine infinite bus (OMIB) equivalent in theory and nature. Compared with such methods as EEAC and SIME, detailed system model of steady state and transient can be considered in SGEAC. Therefore, it has the universality of the numerical integration method. Meanwhile, it is not necessary to identify the equivalent machines to avoid getting wrong stability evaluation. The accuracy of the algorithm is ensured without any assumptions or using hypothetical situations.
In the guarantee algorithm model's accurate situation, the power-angle curve fitting method is proposed to calculate the transient stability margin or the transient instability margin for further speeding transient stability analysis in this paper. The electromagnetic power of single equivalent is expressed by the polynomial function according to the proposed Taylor series expansion analysis in the COI frame by theoretical analysis. The curve between electric power of generator unit and rotor's angle in relative to center of inertia is expanded by Taylor's series based on single generation equivalent area criteria theory (SGEAC). By using SGEAC and combining with time domain simulation method, the disturbed system is simulated for a very short time period. According to the simulation result, the curve between electric power of generator unit and rotor's angle in relative to center of inertia is fitted. Maximum deceleration area or maximum acceleration area of each unit is obtained according to the fitted curves and then the stability margin and instability margin for the system are obtained. This method has advantage of good accuracy and adaptability of time-domain simulation method and by using the method, the energy type stability margin is obtained. A fast transient stability prediction method based on the WAMS process measurement is proposed in this paper. It can quickly predict the system stability margin, the moment when the system loses stability and control devices' response time by scrolling the measurement data which have been measured by the local PMU. Practical system analysis shows that the method is very efficient, and it should have wide engineering applications for on-line stability monitoring.
In addition to evaluate the stability of the system, another important issue is that if the system will lose stability, how to apply the appropriate amount of control to prevent system instability or to achieve the intended target, which is another important part of this paper. It involves quantitative analysis of power system stability and quantitative indicators' impact on control variables, even in the offline environment, this is a difficult, it will be more difficult in real-time environment that require fast given the appropriate amount of control. Fianally, a method is proposed for allocating generation so as to maximize power transfer between areas of interconnected systems under transient stability constraints. The proposed method is to specify how to give control or adjust strategy by SGEAC. This transient stability-constrained maximum allowable transfer method consists of screening a large number of contingencies, scrutinizing the dangerous ones, calculating the shifting active power generation of critical generators and suggesting generation rescheduling patterns to stabilize them by SGEAC. The method is accurate and adaptable as the time domain simulation method, but also stability margin based on single machine energy can be obtained. Compared with other energy function, it is not necessary to determine the correct two-group mode, can apply in multiply contingencies, multi-swing instability scenarios and different instability modes. It avoids exhaustive search. In addition, by controlling all dangerous contingencies simultaneously, the method succeeds in being fully compatible with requirements for real-time preventive monitoring and control. Lots of example analysis with different losing synchronism modes verified the proposed method.
引文
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