电网状态估计及其扩展的理论研究
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摘要
电网实现调度自动化,状态估计是前提和基础。在SCADA系统日益完善和普及条件下,电网状态估计的理论研究与实践工作不断成熟,从某种意义上讲,电网已步入自动化的时代。然而,伴随GPS的广域量测技术的出现,节能减排政策的出台,以及电网抵御意外扰动水平要求的提高等,对电网状态估计的理论研究与实践来讲,无论从深度上还是广度上都提出若干新的问题,如相量量测单元(PMU)与现有状态估计的关系、贡献及混合估计的方法等问题,从更广角度的计及模拟量、开关量及参量的广义电网状态估计问题,侧重于输电元件能力挖掘的在线动态定值问题,基于在线监测的状态检修技术等实施中涉及的参量、特征量的估计问题等,都需要对现有的电网状态估计理论研究进行再深入和扩展。在此背景下,本文围绕电网状态估计及其扩展展开深入细致的理论研究具有重要意义,研究的内容和取得的进展可总结如下：
(1)分析、研究了PMU的引入对仅依据SCADA系统的电网状态估计带来的影响,并提出了一种相应的解决方法,进一步完善电网状态估计的理论。PMU可以直接测量节点电压相量,即电网状态变量(节点电压幅值和相角),与SCADA量测相比,前者是状态变量的显函数,而后者则是状态变量的隐函数,可见依据SCADA系统的状态估计必须在电网可观测条件下进行,而依据PMU的状态估计可以在局部可观测条件下进行。显然,若PMU量测精度足够高,且实现电网状态可观,则不再需要电网状态估计；若PMU量测精度足够高,但只实现电网局部状态可观,则依据SCADA量测的电网状态估计将视PMU配置情况而得到不同程度简化。针对后者,本文就电网状态估计中可观测性问题,状态估计的算法问题,以及不良数据识别问题等,就PMU引入对电网状态估计带来的影响进行了深入研究。首先,就可观测性问题,由于PMU的引入,使传统分析方法获得显著简化,PMU配置的越充分,可观测性分析就越容易；其次,在假设配置的PMU具有充分精度的基础上,建立依据SCADA量测对未知状态进行估计的缩减状态估计模型和算法；最后,针对该缩减状态估计模型,就PMU量测引入对不良数据识别方法及影响进行了研究,研究与分析发现：在SCADA量测数不变条件下,由于PMU引入使量测冗余度提升,从而使不良数据识别能力增强；再者,当PMU量测有误差时,实施缩减模型估计前,提出结合SCADA量测对PMU配置点附近展开混合估计以校正该节点状态精度的方法。
(2)针对PMU和SCADA在电网中共存的情况,提出了一种电网状态估计分解协调的模型和算法。综上,PMU至少可实现系统局部可观,此性质必然产生电网状态量的自动划分,即出现了围绕PMU配置点集的若干可观测性子系统。基于这一思路,从电网状态估计快速性角度出发,提出电网状态估计分解协调的快速算法。分解是指依据PMU配置的可观测子系统的划分,协调是指各子系统如何达到无缝的衔接,在快速估计下达到与整体估计一样的效果。具体思想体现在：依据电网中配置PMU的节点,可将电网划分为两类子岛,即直接电气连接的PMU配置节点集合的割集构成的子系统(定义为PMU可观测岛),和仅含有依据SCADA系统量测量,且不包含PMU配置节点的其它节点构成的割集(定义为SCADA可观测岛)。这样,PMU可观测岛与SCADA可观测岛交集所对应的节点则称为边界点,PMU可观测岛与SCADA可观测岛之间的元件称之为联络元件。在上述思想基础上,对系统进行划分,首先对PMU可观测岛进行估计,得到联络元件上潮流,进而计及联络线路潮流为伪量测,对SCADA可观测岛进行估计,最后协调各子岛参考节点及边界点相角,得到全网统一的状态估计解。
(3)在广义状态估计概念引导下,提出一种识别闭合开关元件状态错误的电网状态估计模型和方法。其核心在于：为识别闭合开关元件构成的拓扑连接错误,提出虚拟特征开关元件的概念,并以此构建不影响识别结果的最小特征电网。在此基础上,以模拟量量测方程构成加权最小二乘的目标函数,将虚拟特征开关元件两端节点的电压差为零作为等式约束条件,从而构造带有约束的加权最小二乘的电网状态估计模型,并对此非线性优化问题进行求解；接着,在模拟量量测误差分布概率已知条件下,分析了拉格朗日乘子的涵义,即任意拉格朗日乘子对应着虚拟零阻抗元件的量测方程,且与模拟量的残差分布之间存在一致性和关联性；通过演绎拉格朗日乘子值与量测残差的概率分布关系,实现了利用模拟量量测间接反映虚拟零阻抗元件状态信息是否有误的目的,最终提出了统一识别模拟量测、闭合开关元件不良数据的方法。同时,论证了在系统仅有一个不良数据的情况下,模拟量量测与开关拓扑两者不良数据识别相互之间并不混淆。由于采用特征虚拟开关元件进行建模,从而有效减小了计算规模,显著提高了计算速度,具有一定的工程应用前景。
(4)针对架空输电线路电热协调方程,在状态估计概念下,建立了基于PMU量测的输电线路温度估计模型,提供输电线路温度实时估计的理论基础。其核心思想是,忽略输电线路载流时温度变化对电抗、电纳的影响,认为仅有电阻会随着运行条件(载流)的改变而变化,在此基础之上通过对电阻的实时估计,间接实现对输电线路温度的实时追踪。若输电线路两端均配置PMU量测装置,则输电线路两端的电流、电压及其相角均为已知,由此依据电工原理,得到直角坐标系下的输电线路量测方程,进而利用线性加权最小二乘方法建立了对输电线路电阻的估计模型。同时,基于输电线路电阻与温度之间的物理解析规律,通过电阻的实时估计,对应便实现了温度的跟踪估计。其中,就误差分布问题,在建立直角坐标系下的量测方程时,PMU直接量测被转换为等值的间接量测,相应的直接误差被转换为间接误差。对此,在已知直接量测误差概率分布的前提下,本文对转换后间接量测误差的分布概率分布进行了推导,就转换后量测误差存在相关性的条件下,分析可知加权最小二乘目标函数值的概率分布特性仍然满足x2分布,即仍可以通过检测目标函数值的方法进行不良数据的识别。总之,该模型和方法简单并易实现,为充分挖掘输电线路的潜在能力提供了一种理论依据。
(5)在动态热定值(DTR)硬技术基础上,结合电热协调(ETC)理论,提出软DTR的思想,建立了基于SCADA信息追踪输电线路热定值的模型和算法。该模型和算法主要体现在：首先依据目前电网,围绕电气特性有丰富量测信息的背景,通过SCADA量测建立了输电线路电阻的扩展状态估计模型；进而,考虑到电阻变化的马尔克夫特性,为充分利用电阻的先验信息,使用相邻时刻的电阻估计值对当前估计结果进行修正以使其平滑并提高跟踪精度,依据电阻与温度之间的物理解析关系,间接获得输电线路的温度；接着,构建带有时变环境参量的简化输电线路热平衡微分方程模型,根据连续的输电线路温度变化轨迹,基于渐消递推最小二乘法实现对时变环境参量的动态估计,最终仅通过电气量测实现了与完整的硬DTR相同的功能；最后,与硬DTR技术相比,通过电阻间接实现输电线路温度趋势的把握和估计,与周围环境条件无直接的依赖关系,使影响精度的量缩减为一个,即精度仅取决于输电线路的电阻。该模型和方法简单、实现容易,只要电网状态估计可行,电网中任一输电元件都可实现软DTR功能。
(6)提出了基于软DTR的“地区电网元件载荷能力的在线定值系统”的框架和平台设计,为完成系统开发提供有利基础,并在山东烟台地区电网得到应用。在运行条件下,电网中输电元件的载荷能力主要受到来自系统运行条件的制约和输电元件本身的物理条件制约。“地区电网元件载荷能力的在线定值系统”主要提供以输电元件温度为载荷能力的评判体系,可为调度、控制决策提供依据,从而实现提高电网输电运行效率、节约资源之目的。其主要功能体现在：基于软DTR下的输电元件温度变化跟踪估计,以及基于输电元件温度变化轨迹的热平衡方程参数的动态估计；在此基础上,将输电元件温度作为扩展状态的在线电热协调潮流分析；计及热载荷制约、电压水平制约及静态功角稳定制约的输电元件载荷能力在线定值计算,实现在线输电元件载荷能力的裕度分析；分析各种预想事件下输电元件能力的变化轨迹,给调度提供预警、紧急状态下校正控制等决策支持。上述系统功能实现的基础是状态估计,本文提供以状态估计为核心的平台,量测信息包含SCADA及PMU混合量测,主要算法包括计及闭合开关元件信息的状态估计,计及PMU量测的协调状态估计,基于PMU的输电线路温度实时估计,基于SCADA量测的输电线路温度估计,以及输电线路热平衡微分方程参数的动态估计等内容。该平台不仅为在线电网输电能力综合评价提供技术支撑,同时也实现了本文理论研究与实践的有机结合。
综上所述,本文就计及PMU量测、计及闭合开关状态、以及输电线路在线定值中涉及状态、参量的估计问题进行了深入而全面的研究与探索,提出相应模型和解决方法,并经山东省烟台地区电网得到验证,在此领域的研究与实践上取得一些进展。当然,该研究从丰富、发展和完善角度看,尚有诸多理论与实际问题有待深入探索和研究。
Network state estimation is the base of power system dispatching automation. The art of network state estimation is becoming mature at theoretical and practical aspect while along with the development of SCADA.To a certain extent, the power system has rounded into the era of automation. However, with the emergence of the wide area measurement technology based on GPS, the promotion of energy conservation and emission reduction policies as well as the continual improvements of the requirement for the ability of power electric system to resist perturbations, the network state estimation has to face the new problems in all aspects, such as research on the relationship between the existing network state estimation and phasor measurement unit(PMU),the contribution of PMU to network state estimation, the mixed algorithm with PMU, the generalized network estimation including analog and digital measurements, parameters as well as characteristic values that accompany with the dynamic thermal rating and electric power equipment condition-based maintenance. Against this background, the network state estimation and its expansions has been studied. The main works and achievements can be summarized as follows:
(1) The impact of PMU on traditional state estimation based solely on the SCADA system is studied and analyzed. An appropriate solution is proposed to improve the power system state estimation theory. PMU can directly get the measurements of bus voltage phasors. In that way, the state variables of system (the bus voltage magnitude and phase angle) are known. Compared with the SCADA measurement, the PMU measurement is the explicit function of state variables, while the latter is the implicit function. State estimation based on SCADA system can run on the conditions that the whole system is observable, but PMU can make the network state observable locally. Obviously, if the PMU measurement accuracy is high enough and can make the whole network state observable completely, the state estimation will be no longer needed. If PMU measurement accuracy is high enough but only allocated at part of power system, the network state estimation based on SCADA would be simple. For the latter, this thesis tried to explore the impact of PMU on the network state estimation such as observabilty analysis, algorithm research as well as bad data identification. Firstly, due to the introduction of PMU, the traditional observability analysis methods obtain a significant simplification. The more PMU measurements allocated, the easier the observabiltiy analysis will be. Secondly, under the assumption that PMU measurement has sufficient precision, the reduced state estimation model and algorithms based on SCADA can be presented to estimate the unknown state variables. And finally, against the reduced state estimation model, the impaction of PMU measurements on bad data identification methods has been discussed. It is found that the redundancy level is raised as the amount of PMU measurements increases. And the identification ability is enhanced. Furthermore, once the PMU measurement has error, the state variables from PMU need to be corrected, and the local mixed state estimation is proposed to improve the accuracy.
(2) For the situation of the PMU and SCADA measurements co-exist, a decomposition and coordination state estimation algorithm is presented. Local estimation can be processed with the help of PMU measurements, and the system can be divided automatically into a number of observable subsystems around PMU. Based on this idea, this thesis proposes a decomposition and coordination state estimation algorithm in view of quicker calculating speed. Decomposition relies on the location of PMU, while coordination is responsible for linking different sub-systems smoothly and unifying the result at the same reference bus angle. In short, quicker speed is achieved. The process is listed as follows:According to the configuration of PMU in the power system, the power system can be divided into two kinds of subsystem. The PMU observable island is a cut-set that formed by direct electrical connection of the PMU bus, while the SCADA observable island is cut-set containing only SCADA measurements and buses without PMU. In This way, The boundary bus is corresponding to the intersection of PMU observable island and the SCADA island, and connect element lies between the two. After the system is divided, all PMU observable islands are estimated and power flow on connect element is obtained. Then, taking into account the result as pseudo-measurements, the estimation is run on the SCADA observable islands. Finally, the angles of the reference bus and boundary buses in subsystems are coordinated to the unified solution with the same reference bus.
(3) Under the guidance of the concept of generalized state estimation, a state estimation model and method is proposed to identifying closed switch element status. In order to identify the topology error related to closed switches, the concept of the virtual feature switch is put forward to build the minimum feature network, which does not affect the quality of the identification. In addition to analog measurements, zero-voltage-drop for virtual closed switch as equality constraint is added to formulate the model of state estimation which is solved as a nonlinear optimization problem with equality constraints. Then, on the condition that the analog measurements error probability distributions are known, the meaning of Lagrange multipliers is expressed, that is to say the Lagrange multiplier corresponds to the virtual zero-impedance component measurement equation, and Lagrange multiplier distribution has consistency and relevance with the residual distribution. The relation between residual and Lagrange multiplier is used to find error information of zero-impedance component. A unified reconignition of analog measurement and close switch is ultimately obtained. At same time, the thesis verifies that bad data identification of whether analog measurement or switch status is not confused with each other when there is only one bad data in the system. Because the model is build from virtual characteristic switches, the size of the calculation is effectively reduced and calculation speed is increased significantly, which means the method has a certain practical engineering prospects.
(4) With concept of the state estimation, the temperature estimation model of the transmission line is established with PMU measurements and electro-thermal coordination equations of overhead transmission line, which provides real-time estimation theory of the transmission line temperature. The key idea is, among line parameters such as resistance, admittance and conductance etc, which only resistance will vary with the temperature. Under operating condition, real-time tracking of temperature can be indirectly achieved by resistance parameter estimation. If the terminals of transmission lines are equipped with PMU, the current and voltage phase of transmission line at both terminals are known. According to principles of electric engineering, measurement equations are formed in Cartesian coordinates. Then, the linear weighted least squares method is established on the transmission line resistance. Based on the rule of resistance and the temperature, the temperature tracking will be achieved by estimating the resistance of transmission line in real-time. When direct PMU measurements are converted to equivalent indirect measurements, the corresponding errors are converted too. By the known the probability distribution of directly measurements' errors, the distribution of indirect measurements'errors is deduced. The probability distribution of the performance index is also analyzed when measurements'errors are interrelated. The result shows that the performance index is still to meet the distribution of x2, which means that the traditional method of bad data identification is still valid. So, the model and method are simple and easy to realize, which provide a theoretical basis for fully exploiting the potential capacity of transmission lines.
(5) On the basis of hardware of the dynamic thermal rating (DTR) technologies and combined with electro-thermal coordination (ETC) theory, the conception of soft-DTR is introduced. The model and algorithm of tracking transmission line rating are established from the SCADA information. The model and algorithm are fulfilled as follows:First, there is rich electrical information of the transmission line in power system, by which the extended estimation with transmission line resistance is established. Furthermore, in order to take full use of resistance prior information, considering the Markov properties of resistance changing, the current estimated value is amended and smoothed by the adjacent moment value, and the tracking accuracy is improved. The temperature of transmission line is obtained indirectly by the analytic relationship between resistance and the temperature. Then, a simplified heat balance differential equation (HBE) model of transmission lines is set up with time-varying environmental parameters. According to a continuous transmission line temperature series, the dynamic estimation of time-varying environmental parameters is realized by fading recursive least squares method. Then, complete functions of hardware DTR functions are achieved only by electrical measurements. Finally, in comparison with hard DTR technology, the trend of temperature is grasped by the line resistance indirectly, which means that the temperature accuracy is influenced by the resistance of transmission lines rather than the surrounding environmental conditions. The model and method are simple and easily implemented, and the soft-DTR of each transmission component can be realized as long as the estimation is workable.
(6) Based on soft-DTR, the framework and platform of the project named "On-line evaluation system of the transmission components loadability at regional power grid" is designed, which provides a favorable basis for the whole system.Now it is applied in Yantai power grid of Shandong Province. In the operating conditions, the loadability of power transmission component is mainly constrained by operating conditions in the power system and itself physical condition. The project of "On-line evaluation system of the transmission components loadability at regional power grid" is to judge transmission components loadability mainly by the temperature for the scheduling and control decision-making.At the same time, the transmission efficiency of grid is improved and the resource is saved. The main functions of the project are listed as follows:Based on the soft-DTR, the temperature of transmission component is estimated, as well as the dynamic parameters of HBE. Then, electro-thermal coordination power flow is run with the temperature as extented state. Taking into account the thermal load constraints, voltage level constraints and static power angle stability constraints, the evaluation of the transmission line loadability is realized.The loadability margin is also analyzed. Under the anticipated events, the varying of the transmission component loadability is tracked, which provides decision support for scheduling and early warning. The foundation of the above-mentioned functions is state estimation. This thesis provides a platform based on state estimation with SCADA and PMU measurements. The algorithms include: the algorithm of state estimation with the identification of closed breakers information, state estimation including PMU, tracking estimation of transmission line temperature based on PMU or SCADA, tracking of transmission line dynamic thermal rating and so on. The platform not only provides technical support for the comprehensive evaluation of power transmission line, but also realizes the organic combination of the theory and practice.
In conclusion, taking into account the PMU measurements, switch status, and state related with transmission line rating evaluation, the thesis has done comprehensive study and proposed the model and appropriate solutions. The study has been verified by the application at Yantai power grid in Shandong Province. A little progress has been made in this field. Of course, from the point view of prosperity, development and improvement, there are still a number of theoretical and practical issues remain to be explored and studied further.
(1)分析、研究了PMU的引入对仅依据SCADA系统的电网状态估计带来的影响,并提出了一种相应的解决方法,进一步完善电网状态估计的理论。PMU可以直接测量节点电压相量,即电网状态变量(节点电压幅值和相角),与SCADA量测相比,前者是状态变量的显函数,而后者则是状态变量的隐函数,可见依据SCADA系统的状态估计必须在电网可观测条件下进行,而依据PMU的状态估计可以在局部可观测条件下进行。显然,若PMU量测精度足够高,且实现电网状态可观,则不再需要电网状态估计；若PMU量测精度足够高,但只实现电网局部状态可观,则依据SCADA量测的电网状态估计将视PMU配置情况而得到不同程度简化。针对后者,本文就电网状态估计中可观测性问题,状态估计的算法问题,以及不良数据识别问题等,就PMU引入对电网状态估计带来的影响进行了深入研究。首先,就可观测性问题,由于PMU的引入,使传统分析方法获得显著简化,PMU配置的越充分,可观测性分析就越容易；其次,在假设配置的PMU具有充分精度的基础上,建立依据SCADA量测对未知状态进行估计的缩减状态估计模型和算法；最后,针对该缩减状态估计模型,就PMU量测引入对不良数据识别方法及影响进行了研究,研究与分析发现：在SCADA量测数不变条件下,由于PMU引入使量测冗余度提升,从而使不良数据识别能力增强；再者,当PMU量测有误差时,实施缩减模型估计前,提出结合SCADA量测对PMU配置点附近展开混合估计以校正该节点状态精度的方法。
(2)针对PMU和SCADA在电网中共存的情况,提出了一种电网状态估计分解协调的模型和算法。综上,PMU至少可实现系统局部可观,此性质必然产生电网状态量的自动划分,即出现了围绕PMU配置点集的若干可观测性子系统。基于这一思路,从电网状态估计快速性角度出发,提出电网状态估计分解协调的快速算法。分解是指依据PMU配置的可观测子系统的划分,协调是指各子系统如何达到无缝的衔接,在快速估计下达到与整体估计一样的效果。具体思想体现在：依据电网中配置PMU的节点,可将电网划分为两类子岛,即直接电气连接的PMU配置节点集合的割集构成的子系统(定义为PMU可观测岛),和仅含有依据SCADA系统量测量,且不包含PMU配置节点的其它节点构成的割集(定义为SCADA可观测岛)。这样,PMU可观测岛与SCADA可观测岛交集所对应的节点则称为边界点,PMU可观测岛与SCADA可观测岛之间的元件称之为联络元件。在上述思想基础上,对系统进行划分,首先对PMU可观测岛进行估计,得到联络元件上潮流,进而计及联络线路潮流为伪量测,对SCADA可观测岛进行估计,最后协调各子岛参考节点及边界点相角,得到全网统一的状态估计解。
(3)在广义状态估计概念引导下,提出一种识别闭合开关元件状态错误的电网状态估计模型和方法。其核心在于：为识别闭合开关元件构成的拓扑连接错误,提出虚拟特征开关元件的概念,并以此构建不影响识别结果的最小特征电网。在此基础上,以模拟量量测方程构成加权最小二乘的目标函数,将虚拟特征开关元件两端节点的电压差为零作为等式约束条件,从而构造带有约束的加权最小二乘的电网状态估计模型,并对此非线性优化问题进行求解；接着,在模拟量量测误差分布概率已知条件下,分析了拉格朗日乘子的涵义,即任意拉格朗日乘子对应着虚拟零阻抗元件的量测方程,且与模拟量的残差分布之间存在一致性和关联性；通过演绎拉格朗日乘子值与量测残差的概率分布关系,实现了利用模拟量量测间接反映虚拟零阻抗元件状态信息是否有误的目的,最终提出了统一识别模拟量测、闭合开关元件不良数据的方法。同时,论证了在系统仅有一个不良数据的情况下,模拟量量测与开关拓扑两者不良数据识别相互之间并不混淆。由于采用特征虚拟开关元件进行建模,从而有效减小了计算规模,显著提高了计算速度,具有一定的工程应用前景。
(4)针对架空输电线路电热协调方程,在状态估计概念下,建立了基于PMU量测的输电线路温度估计模型,提供输电线路温度实时估计的理论基础。其核心思想是,忽略输电线路载流时温度变化对电抗、电纳的影响,认为仅有电阻会随着运行条件(载流)的改变而变化,在此基础之上通过对电阻的实时估计,间接实现对输电线路温度的实时追踪。若输电线路两端均配置PMU量测装置,则输电线路两端的电流、电压及其相角均为已知,由此依据电工原理,得到直角坐标系下的输电线路量测方程,进而利用线性加权最小二乘方法建立了对输电线路电阻的估计模型。同时,基于输电线路电阻与温度之间的物理解析规律,通过电阻的实时估计,对应便实现了温度的跟踪估计。其中,就误差分布问题,在建立直角坐标系下的量测方程时,PMU直接量测被转换为等值的间接量测,相应的直接误差被转换为间接误差。对此,在已知直接量测误差概率分布的前提下,本文对转换后间接量测误差的分布概率分布进行了推导,就转换后量测误差存在相关性的条件下,分析可知加权最小二乘目标函数值的概率分布特性仍然满足x2分布,即仍可以通过检测目标函数值的方法进行不良数据的识别。总之,该模型和方法简单并易实现,为充分挖掘输电线路的潜在能力提供了一种理论依据。
(5)在动态热定值(DTR)硬技术基础上,结合电热协调(ETC)理论,提出软DTR的思想,建立了基于SCADA信息追踪输电线路热定值的模型和算法。该模型和算法主要体现在：首先依据目前电网,围绕电气特性有丰富量测信息的背景,通过SCADA量测建立了输电线路电阻的扩展状态估计模型；进而,考虑到电阻变化的马尔克夫特性,为充分利用电阻的先验信息,使用相邻时刻的电阻估计值对当前估计结果进行修正以使其平滑并提高跟踪精度,依据电阻与温度之间的物理解析关系,间接获得输电线路的温度；接着,构建带有时变环境参量的简化输电线路热平衡微分方程模型,根据连续的输电线路温度变化轨迹,基于渐消递推最小二乘法实现对时变环境参量的动态估计,最终仅通过电气量测实现了与完整的硬DTR相同的功能；最后,与硬DTR技术相比,通过电阻间接实现输电线路温度趋势的把握和估计,与周围环境条件无直接的依赖关系,使影响精度的量缩减为一个,即精度仅取决于输电线路的电阻。该模型和方法简单、实现容易,只要电网状态估计可行,电网中任一输电元件都可实现软DTR功能。
(6)提出了基于软DTR的“地区电网元件载荷能力的在线定值系统”的框架和平台设计,为完成系统开发提供有利基础,并在山东烟台地区电网得到应用。在运行条件下,电网中输电元件的载荷能力主要受到来自系统运行条件的制约和输电元件本身的物理条件制约。“地区电网元件载荷能力的在线定值系统”主要提供以输电元件温度为载荷能力的评判体系,可为调度、控制决策提供依据,从而实现提高电网输电运行效率、节约资源之目的。其主要功能体现在：基于软DTR下的输电元件温度变化跟踪估计,以及基于输电元件温度变化轨迹的热平衡方程参数的动态估计；在此基础上,将输电元件温度作为扩展状态的在线电热协调潮流分析；计及热载荷制约、电压水平制约及静态功角稳定制约的输电元件载荷能力在线定值计算,实现在线输电元件载荷能力的裕度分析；分析各种预想事件下输电元件能力的变化轨迹,给调度提供预警、紧急状态下校正控制等决策支持。上述系统功能实现的基础是状态估计,本文提供以状态估计为核心的平台,量测信息包含SCADA及PMU混合量测,主要算法包括计及闭合开关元件信息的状态估计,计及PMU量测的协调状态估计,基于PMU的输电线路温度实时估计,基于SCADA量测的输电线路温度估计,以及输电线路热平衡微分方程参数的动态估计等内容。该平台不仅为在线电网输电能力综合评价提供技术支撑,同时也实现了本文理论研究与实践的有机结合。
综上所述,本文就计及PMU量测、计及闭合开关状态、以及输电线路在线定值中涉及状态、参量的估计问题进行了深入而全面的研究与探索,提出相应模型和解决方法,并经山东省烟台地区电网得到验证,在此领域的研究与实践上取得一些进展。当然,该研究从丰富、发展和完善角度看,尚有诸多理论与实际问题有待深入探索和研究。
Network state estimation is the base of power system dispatching automation. The art of network state estimation is becoming mature at theoretical and practical aspect while along with the development of SCADA.To a certain extent, the power system has rounded into the era of automation. However, with the emergence of the wide area measurement technology based on GPS, the promotion of energy conservation and emission reduction policies as well as the continual improvements of the requirement for the ability of power electric system to resist perturbations, the network state estimation has to face the new problems in all aspects, such as research on the relationship between the existing network state estimation and phasor measurement unit(PMU),the contribution of PMU to network state estimation, the mixed algorithm with PMU, the generalized network estimation including analog and digital measurements, parameters as well as characteristic values that accompany with the dynamic thermal rating and electric power equipment condition-based maintenance. Against this background, the network state estimation and its expansions has been studied. The main works and achievements can be summarized as follows:
(1) The impact of PMU on traditional state estimation based solely on the SCADA system is studied and analyzed. An appropriate solution is proposed to improve the power system state estimation theory. PMU can directly get the measurements of bus voltage phasors. In that way, the state variables of system (the bus voltage magnitude and phase angle) are known. Compared with the SCADA measurement, the PMU measurement is the explicit function of state variables, while the latter is the implicit function. State estimation based on SCADA system can run on the conditions that the whole system is observable, but PMU can make the network state observable locally. Obviously, if the PMU measurement accuracy is high enough and can make the whole network state observable completely, the state estimation will be no longer needed. If PMU measurement accuracy is high enough but only allocated at part of power system, the network state estimation based on SCADA would be simple. For the latter, this thesis tried to explore the impact of PMU on the network state estimation such as observabilty analysis, algorithm research as well as bad data identification. Firstly, due to the introduction of PMU, the traditional observability analysis methods obtain a significant simplification. The more PMU measurements allocated, the easier the observabiltiy analysis will be. Secondly, under the assumption that PMU measurement has sufficient precision, the reduced state estimation model and algorithms based on SCADA can be presented to estimate the unknown state variables. And finally, against the reduced state estimation model, the impaction of PMU measurements on bad data identification methods has been discussed. It is found that the redundancy level is raised as the amount of PMU measurements increases. And the identification ability is enhanced. Furthermore, once the PMU measurement has error, the state variables from PMU need to be corrected, and the local mixed state estimation is proposed to improve the accuracy.
(2) For the situation of the PMU and SCADA measurements co-exist, a decomposition and coordination state estimation algorithm is presented. Local estimation can be processed with the help of PMU measurements, and the system can be divided automatically into a number of observable subsystems around PMU. Based on this idea, this thesis proposes a decomposition and coordination state estimation algorithm in view of quicker calculating speed. Decomposition relies on the location of PMU, while coordination is responsible for linking different sub-systems smoothly and unifying the result at the same reference bus angle. In short, quicker speed is achieved. The process is listed as follows:According to the configuration of PMU in the power system, the power system can be divided into two kinds of subsystem. The PMU observable island is a cut-set that formed by direct electrical connection of the PMU bus, while the SCADA observable island is cut-set containing only SCADA measurements and buses without PMU. In This way, The boundary bus is corresponding to the intersection of PMU observable island and the SCADA island, and connect element lies between the two. After the system is divided, all PMU observable islands are estimated and power flow on connect element is obtained. Then, taking into account the result as pseudo-measurements, the estimation is run on the SCADA observable islands. Finally, the angles of the reference bus and boundary buses in subsystems are coordinated to the unified solution with the same reference bus.
(3) Under the guidance of the concept of generalized state estimation, a state estimation model and method is proposed to identifying closed switch element status. In order to identify the topology error related to closed switches, the concept of the virtual feature switch is put forward to build the minimum feature network, which does not affect the quality of the identification. In addition to analog measurements, zero-voltage-drop for virtual closed switch as equality constraint is added to formulate the model of state estimation which is solved as a nonlinear optimization problem with equality constraints. Then, on the condition that the analog measurements error probability distributions are known, the meaning of Lagrange multipliers is expressed, that is to say the Lagrange multiplier corresponds to the virtual zero-impedance component measurement equation, and Lagrange multiplier distribution has consistency and relevance with the residual distribution. The relation between residual and Lagrange multiplier is used to find error information of zero-impedance component. A unified reconignition of analog measurement and close switch is ultimately obtained. At same time, the thesis verifies that bad data identification of whether analog measurement or switch status is not confused with each other when there is only one bad data in the system. Because the model is build from virtual characteristic switches, the size of the calculation is effectively reduced and calculation speed is increased significantly, which means the method has a certain practical engineering prospects.
(4) With concept of the state estimation, the temperature estimation model of the transmission line is established with PMU measurements and electro-thermal coordination equations of overhead transmission line, which provides real-time estimation theory of the transmission line temperature. The key idea is, among line parameters such as resistance, admittance and conductance etc, which only resistance will vary with the temperature. Under operating condition, real-time tracking of temperature can be indirectly achieved by resistance parameter estimation. If the terminals of transmission lines are equipped with PMU, the current and voltage phase of transmission line at both terminals are known. According to principles of electric engineering, measurement equations are formed in Cartesian coordinates. Then, the linear weighted least squares method is established on the transmission line resistance. Based on the rule of resistance and the temperature, the temperature tracking will be achieved by estimating the resistance of transmission line in real-time. When direct PMU measurements are converted to equivalent indirect measurements, the corresponding errors are converted too. By the known the probability distribution of directly measurements' errors, the distribution of indirect measurements'errors is deduced. The probability distribution of the performance index is also analyzed when measurements'errors are interrelated. The result shows that the performance index is still to meet the distribution of x2, which means that the traditional method of bad data identification is still valid. So, the model and method are simple and easy to realize, which provide a theoretical basis for fully exploiting the potential capacity of transmission lines.
(5) On the basis of hardware of the dynamic thermal rating (DTR) technologies and combined with electro-thermal coordination (ETC) theory, the conception of soft-DTR is introduced. The model and algorithm of tracking transmission line rating are established from the SCADA information. The model and algorithm are fulfilled as follows:First, there is rich electrical information of the transmission line in power system, by which the extended estimation with transmission line resistance is established. Furthermore, in order to take full use of resistance prior information, considering the Markov properties of resistance changing, the current estimated value is amended and smoothed by the adjacent moment value, and the tracking accuracy is improved. The temperature of transmission line is obtained indirectly by the analytic relationship between resistance and the temperature. Then, a simplified heat balance differential equation (HBE) model of transmission lines is set up with time-varying environmental parameters. According to a continuous transmission line temperature series, the dynamic estimation of time-varying environmental parameters is realized by fading recursive least squares method. Then, complete functions of hardware DTR functions are achieved only by electrical measurements. Finally, in comparison with hard DTR technology, the trend of temperature is grasped by the line resistance indirectly, which means that the temperature accuracy is influenced by the resistance of transmission lines rather than the surrounding environmental conditions. The model and method are simple and easily implemented, and the soft-DTR of each transmission component can be realized as long as the estimation is workable.
(6) Based on soft-DTR, the framework and platform of the project named "On-line evaluation system of the transmission components loadability at regional power grid" is designed, which provides a favorable basis for the whole system.Now it is applied in Yantai power grid of Shandong Province. In the operating conditions, the loadability of power transmission component is mainly constrained by operating conditions in the power system and itself physical condition. The project of "On-line evaluation system of the transmission components loadability at regional power grid" is to judge transmission components loadability mainly by the temperature for the scheduling and control decision-making.At the same time, the transmission efficiency of grid is improved and the resource is saved. The main functions of the project are listed as follows:Based on the soft-DTR, the temperature of transmission component is estimated, as well as the dynamic parameters of HBE. Then, electro-thermal coordination power flow is run with the temperature as extented state. Taking into account the thermal load constraints, voltage level constraints and static power angle stability constraints, the evaluation of the transmission line loadability is realized.The loadability margin is also analyzed. Under the anticipated events, the varying of the transmission component loadability is tracked, which provides decision support for scheduling and early warning. The foundation of the above-mentioned functions is state estimation. This thesis provides a platform based on state estimation with SCADA and PMU measurements. The algorithms include: the algorithm of state estimation with the identification of closed breakers information, state estimation including PMU, tracking estimation of transmission line temperature based on PMU or SCADA, tracking of transmission line dynamic thermal rating and so on. The platform not only provides technical support for the comprehensive evaluation of power transmission line, but also realizes the organic combination of the theory and practice.
In conclusion, taking into account the PMU measurements, switch status, and state related with transmission line rating evaluation, the thesis has done comprehensive study and proposed the model and appropriate solutions. The study has been verified by the application at Yantai power grid in Shandong Province. A little progress has been made in this field. Of course, from the point view of prosperity, development and improvement, there are still a number of theoretical and practical issues remain to be explored and studied further.
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