含风电的电力系统备用决策及小扰动随机稳定分析
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摘要
风力发电是开发利用可再生清洁能源的主要形式。大力发展风电对优化能源结构、实现能源供应多元化、应对气候变化、保护生态环境具有非常重要的意义。大规模、集中开发,远距离、高电压输送是我国风电发展的主要特征。与常规电源的可调可控相比,风电机组的调节能力弱且其出力具有随机波动性,大规模风电接入给电力系统的安全稳定运行带来很大影响。传统的基于确定性状态方程的稳定性分析方法在解决风电随机波动引发的稳定问题时受到局限,有必要借助随机微分方程和随机稳定理论对风电接入后的电力系统稳定性进行系统研究。而目前这方面的研究还很薄弱。本文针对风电随机性进入电力系统状态方程的不同层面,有针对性地对含风电电力系统的运行优化和小扰动随机稳定机理展开探索研究：针对风电不确定性给系统运行平衡点带来的影响,研究风电不确定性建模和含风电电力系统的备用和调度决策模型；以风电机组随机动态建模为突破口,基于随机微分方程理论研究随机激励和随机系数下的电力系统小扰动随机稳定性建模及分析方法。研究旨在将电力系统稳定性建模和分析方法拓展到随机空间下。具体的研究内容及成果如下：
1.基于场景法对风电功率的不确定性进行了建模研究。针对传统场景缩减算法无法有效处理海量初始场景的问题,提出了一种基于粒子群优化算法的改进场景缩减方法。该场景缩减算法的寻优空间是整个初始场景集,但粒子迭代寻优时的速度更新仅与自身之前的最优位置及粒子群中和其Kantorovich距离最小的粒子有关,相比传统算法,寻优时不需要对初始场景集进行遍历,计算耗时大大减少,从而有效解决了海量场景的缩减问题,为进一步的含风电电力系统优化调度研究打下了基础。
2.针对风电出力不确定性对系统运行平衡点的影响,研究了含风电电力系统的备用决策和调度问题。基于故障场景集提出了一种综合反映电源、负荷不确定性的可靠性指标,并推导了风电接入后系统备用需求的量化表达式,进而建立了含风电的电力系统发电和备用协调优化模型。利用该模型,不仅可以得到系统每个时段所需的运行备用总量,还可得到每个时段机组间的最优发电和备用分配方案。通过算例仿真验证了模型的有效性。所提方法很好地解决大规模风电接入后备用容量的量化和分配问题,给出的优化调度方案,为计算系统稳态运行平衡点提供了依据。
3.在梳理随机微分方程及随机稳定理论的基础上,研究了受随机激励影响的电力系统小扰动随机稳定机理。将异步风机机械功率视为随机过程,基于Ito随机微分方程建立了随机激励下的异步风力发电机动态模型,该模型克服了Riemann积分无法处理被积函数中随机项的局限,将电力系统的动态模型由确定性的常微分方程框架拓广到了随机微分方程框架下；在此基础上提出并证明了系统随机均值稳定和均方稳定的判据；并进一步推导得到了系统小扰动响应过程期望和方差的计算方法。推导得到的系统状态变量统计特征解析表达式准确地描述了随机激励下系统的动态过程。论文还通过数值方法进行了仿真验证,证明了所提分析方法的有效性和合理性。
4.研究了考虑随机系数的电力系统小扰动随机稳定机理。进一步考虑风机随机功率波动与系统其它电气量之间的耦合作用导致的状态方程系数的随机性,建立了基于Ito随机微分方程的含随机系数的系统动态模型；应用Ito公式将该系统的随机均方稳定性问题转化为确定性系统的均值稳定性问题,利用Lyapunov函数证明了这种系统的随机均方稳定判据；之后结合电力系统随机参数灵敏度分析方法得到了系统随机稳定概率的计算方法；并通过算例仿真验证了所提方法的合理性和有效性。该方法可有效且快速的计算有随机系数的电力系统稳定概率,其本质是解析的,虽然结果保守,但方法严谨可靠,且计算量较小。
Wind power generation, as a kind of clean and renewable energy, is the most important form of wind energy utilization. The development of wind power generation has a great significance to improving energy structure, diversification of energy supply, combating climate change and environment protection. Large scale, centralized exploitation, long distance and high voltage transmission are the key features of wind power development currently. Compared to schedulable and controllable conventional power source, the stochastic and intermittent nature of wind power has brought significant impact on power system operation and stability. Conventional stability analysis methods which are based on deterministic state equations are sometimes incapable of dealing with the stability problems caused by the stochastic fluctuation of wind power. It is necessary to introduce stochastic differential equation and stochastic stability theory to study the stability of power systems with large scale wind power generation. Focused on the different aspects of the impacts of stochastic wind power on system state equations, this paper presents an in-depth research on the stochastic small signal stability and operating optimization of power systems with wind power generation. As to the impact of wind power uncertaity on system equilibrium point, the wind power uncertainty modelling and power system generation dispatch optimization problem is investigated; based on stochastic differential equation theory, this paper carries out a research on the stochastic dynamic modeling of wind turbine generators, and furthuremore studies the stability modeling and analysis methods for power systems with stochastic excitation and stochastic coefficients respectively. The research aims at expanding stability theory from deterministic environment to stochastic environment. Detailed research outcomes are as follows:
1.A wind power uncertainty modeling method is proposed. Aiming at overcoming the drawback of existing scenario reduction methods, which is that they are incapable of dealing with extremely massive initial scenarios, this paper proposes an improved scenario reduction method based on PSO algorithm. The search space of the method is the whole initial scenario set, but the update of velocity and position of each particle are only affected by its previous best position and the Kantorovich Distance between the rest particles of the swarm. Compared to existing method, it no longer needs to traverse the whole initial scenario set during each iteration, which can greatly decrease computing time and effectively solve the extremely massive initial scenarios reduction problem, which laid a foundation of further research on generation dispatch with wind power generation.
2. Aiming at the impact of wind power uncertainty on system equilibrium point, the generation and reserve dispatch optimization of power system with wind power generation is studied. A reliability index which considers the reliability requirements of different types of load is proposed based on fault scenarios. Furthermore, the quantification formula of system reserve requirement is deduced based on the reliability index considering the forced outage rate, load forecast error and wind power forecast error. The reserve quantification formula is then used as a constraint to establish a coordinated power generation and reserve dispatch model of power system with wind farms. Through optimization, not only can we get the reserve requirement and total reserve supplied by the system of each period, but also the optimal reserve allocation among thermal units. The effectiveness and accuracy of the model are validated through simulations. The impact of wind power integrated to the system and substitution of conventional units are also discussed. The proposed method can properly handle the reserve quantification and allocation problem with large-scale wind power, enhance system operation stability and provide a basis for calculation of system equilibrium point, which is the foundation of further stability analysis research.
3. Based on the Ito stochastic differential equation theory and stochastic stability theory, the stochastic small signal stability mechanism of power systems as affected by stochastic excitation is analyzed. The mechanical power input of asynchronous wind turbine is considered as a stochastic process, and the stochastic dynamic models of asynchronous wind turbine generators considering stochatic excitation are established. These models have avoided the disadvantage of Riemann integral (Riemann integral is unable to deal with the stochastic element in the integrand), and expanded the power system dynamic model from deterministic ordinary differential equation frame to stochastic differential equation frame. Furthermore, the system stochastic mean stability and mean square stability criterion are proposed and proved; furthermore, the expectation and variance of system response are obtained by mathematical deduction. The proposed stability criterion is simple and clear; the calculation method of statistical features of system response can help better depict the dynamic response of systems with stochastic excitation and understand the system operating condition. Numerical simulations are performed to verify the effectiveness and accuracy of the proposed method.
4. The stochastic small signal stability mechanism of power systems considering the random coefficients is analyzed. The impacts of stochastic wind mechanical power on coefficients of system state equations are considered and a system dynamic model with random coefficients is estabilished based on Ito stochastic differential equation. By using Ito formula, the stochastic mean square stability problem of this system is converted to mean stability problem of deterministic system. The stochastic mean square stability criterion is proved using Lyapunov function; furthermore, the system stochastic stability probability calculation method is obtained by using power system stochastic parameter sensitivity analysis method. The effectiveness and accuracy of the proposed method are validated by numerical simulation. This method can calculate the system stochastic mean square stability probability fast and effectively. Although the results are a little conservative, the method is strict and reliable and has low time cost due to it is analytical.
1.基于场景法对风电功率的不确定性进行了建模研究。针对传统场景缩减算法无法有效处理海量初始场景的问题,提出了一种基于粒子群优化算法的改进场景缩减方法。该场景缩减算法的寻优空间是整个初始场景集,但粒子迭代寻优时的速度更新仅与自身之前的最优位置及粒子群中和其Kantorovich距离最小的粒子有关,相比传统算法,寻优时不需要对初始场景集进行遍历,计算耗时大大减少,从而有效解决了海量场景的缩减问题,为进一步的含风电电力系统优化调度研究打下了基础。
2.针对风电出力不确定性对系统运行平衡点的影响,研究了含风电电力系统的备用决策和调度问题。基于故障场景集提出了一种综合反映电源、负荷不确定性的可靠性指标,并推导了风电接入后系统备用需求的量化表达式,进而建立了含风电的电力系统发电和备用协调优化模型。利用该模型,不仅可以得到系统每个时段所需的运行备用总量,还可得到每个时段机组间的最优发电和备用分配方案。通过算例仿真验证了模型的有效性。所提方法很好地解决大规模风电接入后备用容量的量化和分配问题,给出的优化调度方案,为计算系统稳态运行平衡点提供了依据。
3.在梳理随机微分方程及随机稳定理论的基础上,研究了受随机激励影响的电力系统小扰动随机稳定机理。将异步风机机械功率视为随机过程,基于Ito随机微分方程建立了随机激励下的异步风力发电机动态模型,该模型克服了Riemann积分无法处理被积函数中随机项的局限,将电力系统的动态模型由确定性的常微分方程框架拓广到了随机微分方程框架下；在此基础上提出并证明了系统随机均值稳定和均方稳定的判据；并进一步推导得到了系统小扰动响应过程期望和方差的计算方法。推导得到的系统状态变量统计特征解析表达式准确地描述了随机激励下系统的动态过程。论文还通过数值方法进行了仿真验证,证明了所提分析方法的有效性和合理性。
4.研究了考虑随机系数的电力系统小扰动随机稳定机理。进一步考虑风机随机功率波动与系统其它电气量之间的耦合作用导致的状态方程系数的随机性,建立了基于Ito随机微分方程的含随机系数的系统动态模型；应用Ito公式将该系统的随机均方稳定性问题转化为确定性系统的均值稳定性问题,利用Lyapunov函数证明了这种系统的随机均方稳定判据；之后结合电力系统随机参数灵敏度分析方法得到了系统随机稳定概率的计算方法；并通过算例仿真验证了所提方法的合理性和有效性。该方法可有效且快速的计算有随机系数的电力系统稳定概率,其本质是解析的,虽然结果保守,但方法严谨可靠,且计算量较小。
Wind power generation, as a kind of clean and renewable energy, is the most important form of wind energy utilization. The development of wind power generation has a great significance to improving energy structure, diversification of energy supply, combating climate change and environment protection. Large scale, centralized exploitation, long distance and high voltage transmission are the key features of wind power development currently. Compared to schedulable and controllable conventional power source, the stochastic and intermittent nature of wind power has brought significant impact on power system operation and stability. Conventional stability analysis methods which are based on deterministic state equations are sometimes incapable of dealing with the stability problems caused by the stochastic fluctuation of wind power. It is necessary to introduce stochastic differential equation and stochastic stability theory to study the stability of power systems with large scale wind power generation. Focused on the different aspects of the impacts of stochastic wind power on system state equations, this paper presents an in-depth research on the stochastic small signal stability and operating optimization of power systems with wind power generation. As to the impact of wind power uncertaity on system equilibrium point, the wind power uncertainty modelling and power system generation dispatch optimization problem is investigated; based on stochastic differential equation theory, this paper carries out a research on the stochastic dynamic modeling of wind turbine generators, and furthuremore studies the stability modeling and analysis methods for power systems with stochastic excitation and stochastic coefficients respectively. The research aims at expanding stability theory from deterministic environment to stochastic environment. Detailed research outcomes are as follows:
1.A wind power uncertainty modeling method is proposed. Aiming at overcoming the drawback of existing scenario reduction methods, which is that they are incapable of dealing with extremely massive initial scenarios, this paper proposes an improved scenario reduction method based on PSO algorithm. The search space of the method is the whole initial scenario set, but the update of velocity and position of each particle are only affected by its previous best position and the Kantorovich Distance between the rest particles of the swarm. Compared to existing method, it no longer needs to traverse the whole initial scenario set during each iteration, which can greatly decrease computing time and effectively solve the extremely massive initial scenarios reduction problem, which laid a foundation of further research on generation dispatch with wind power generation.
2. Aiming at the impact of wind power uncertainty on system equilibrium point, the generation and reserve dispatch optimization of power system with wind power generation is studied. A reliability index which considers the reliability requirements of different types of load is proposed based on fault scenarios. Furthermore, the quantification formula of system reserve requirement is deduced based on the reliability index considering the forced outage rate, load forecast error and wind power forecast error. The reserve quantification formula is then used as a constraint to establish a coordinated power generation and reserve dispatch model of power system with wind farms. Through optimization, not only can we get the reserve requirement and total reserve supplied by the system of each period, but also the optimal reserve allocation among thermal units. The effectiveness and accuracy of the model are validated through simulations. The impact of wind power integrated to the system and substitution of conventional units are also discussed. The proposed method can properly handle the reserve quantification and allocation problem with large-scale wind power, enhance system operation stability and provide a basis for calculation of system equilibrium point, which is the foundation of further stability analysis research.
3. Based on the Ito stochastic differential equation theory and stochastic stability theory, the stochastic small signal stability mechanism of power systems as affected by stochastic excitation is analyzed. The mechanical power input of asynchronous wind turbine is considered as a stochastic process, and the stochastic dynamic models of asynchronous wind turbine generators considering stochatic excitation are established. These models have avoided the disadvantage of Riemann integral (Riemann integral is unable to deal with the stochastic element in the integrand), and expanded the power system dynamic model from deterministic ordinary differential equation frame to stochastic differential equation frame. Furthermore, the system stochastic mean stability and mean square stability criterion are proposed and proved; furthermore, the expectation and variance of system response are obtained by mathematical deduction. The proposed stability criterion is simple and clear; the calculation method of statistical features of system response can help better depict the dynamic response of systems with stochastic excitation and understand the system operating condition. Numerical simulations are performed to verify the effectiveness and accuracy of the proposed method.
4. The stochastic small signal stability mechanism of power systems considering the random coefficients is analyzed. The impacts of stochastic wind mechanical power on coefficients of system state equations are considered and a system dynamic model with random coefficients is estabilished based on Ito stochastic differential equation. By using Ito formula, the stochastic mean square stability problem of this system is converted to mean stability problem of deterministic system. The stochastic mean square stability criterion is proved using Lyapunov function; furthermore, the system stochastic stability probability calculation method is obtained by using power system stochastic parameter sensitivity analysis method. The effectiveness and accuracy of the proposed method are validated by numerical simulation. This method can calculate the system stochastic mean square stability probability fast and effectively. Although the results are a little conservative, the method is strict and reliable and has low time cost due to it is analytical.
引文
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