潮流跟踪模型和算法及其在输电阻塞管理中的应用
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摘要
电力体制改革促使电力系统经营模式由传统垄断模式逐步发展为发电、输电和配电相分离的输电网开放模式,这给电力系统运行和规划带来了巨大的挑战。在引入竞争、优化资源配置的同时,不可避免地出现了传输管理问题,即输电费用分摊、网损分摊和阻塞管理问题。因此,快速准确地确定各发电机与负荷之间的功率分配关系,确定发电机和负荷对输电线的实际使用程度以及发电机对系统损耗的贡献等,显得日益重要。研究如何准确度量各市场参与者对电力系统的使用程度以公平合理的分摊输电费用和网损,以及如何消除传输阻塞以保证系统安全稳定运行等具有重要的理论意义和现实意义。
本文受到重庆市自然科学基金“电力市场潮流分析的理论和应用研究”和“电力市场输电阻塞管理模型与算法研究”等相关课题的资助,对电力市场环境下潮流跟踪模型和算法以及基于潮流跟踪的输电阻塞管理等进行了深入研究。
针对已有功率跟踪方法需经过大量的搜索、跟踪或等值,需假设跟踪原则的不足,提出一种有效、快速的功率跟踪解析模型及求解算法。构造顺流分配矩阵并分析其对角占优、上三角等特点。建立该矩阵与节点注入功率矩阵、负荷功率矩阵以及发电机出力矩阵间的量化关系。提出发电机对负荷功率分配系数矩阵的概念,建立发电机对负荷功率分配、负荷对发电机功率汲取的解析模型。应用矩阵理论证明了基于顺流分配矩阵的功率跟踪算法的正确性。应用IEEE-RTS、NewEngland39和IEEE-118等测试系统,实现发电机、负荷以及线路间的功率分配,展示了良好的应用效果。
系统输送功率时总会在支路上产生损耗,而在进行功率跟踪时常需将实际有损网络等值为无损网络。为提高潮流跟踪和损耗分摊的准确度,根据电流具有无损的特点,提出一种基于扩展关联矩阵的电流跟踪解析模型及求解算法。给出节点间扩展关联矩阵的概念及构造方法,分析该矩阵行元素之和、列元素之和等优良性质。根据交流潮流结果将实际网络分解为实部和虚部电流网络并建立其对应的扩展关联矩阵。根据发电注入以及负荷电流矩阵计算电流跟踪分配系数矩阵,建立发电机对负荷电流分配的解析模型。基于电流跟踪模型进而得到潮流跟踪和损耗分摊的精确结果。论文用定理保证了电流分配和汲取的正确性,并采用电路理论证明跟踪前后节点电流和回路电压均能分别满足电力网络的KCL和KVL定律。该模型不需分摊原则的假设前提,而是通过矩阵分析直接解析求解,可用于无环流/环流网络。通过对测试系统的计算分析,证实了算法的有效性。
电力系统需时刻保持电力平衡,而电力负荷随时间在不断变化,致使电力系统的潮流以及潮流跟踪的结果也随时间变化。前述功率或电流跟踪模型是在给定运行方式下分析功率的分配和汲取情况,不能满足电力系统运行实时性要求。当发电机组出力或负荷变化时,常需重复进行潮流跟踪计算。为有效避免该重复计算,基于多项式理论和潮流跟踪原理建立了描述功率的汲取和分配随运行方式变化规律的潮流跟踪曲线模型。在系统各种运行方式下,分别应用前述功率和电流跟踪模型采集样本数据,进而运用最小二乘法求解潮流跟踪曲线模型。根据Taylor级数理论得到潮流跟踪动态计算的近似模型。在此基础上提出潮流跟踪灵敏度的概念,以描述机组出力变化对支路功率变化的影响程度。根据潮流跟踪灵敏度以及支路潮流越限量确定阻塞管理中参与调整的机组及其出力调整量,采用逐条支路消去法实现输电阻塞管理。对IEEE-30和IEEE-RTS系统进行潮流跟踪的近似计算以及从单回线路、不同位置线路和多条线路阻塞等角度进行输电阻塞管理分析计算,验证了该方法的有效性和正确性。
电力系统中,任意机组出力的变化都会影响潮流跟踪结果。基于此,结合潮流跟踪曲线的思想建立了反映支路潮流跟踪结果与机组出力间非线性关系的多元非线性回归模型。应用变换思想将非线性回归模型转化为线性回归模型,基于前述潮流跟踪模型和Monte Carlo模拟法产生机组出力和潮流跟踪样本,进而应用最小二乘法求解模型。为避免逐条支路消除法可能出现震荡的不足,采用同时消除法进行阻塞管理,根据多元非线性回归模型,基于Taylor级数得到所有阻塞线路潮流越限量与各机组出力调整量之间的关系,以此构成等式约束条件,从而建立以调整费用最小为目标的输电阻塞管理模型,并用拉格朗日乘子法进行求解。将该方法应用于IEEE-RTS等系统,对单回和多回线路阻塞以及不同线路阻塞等情况,以不同目标函数进行输电阻塞管理,验证了该方法的有效性和正确性。
The reformation of electric power industry has gradually changed the operation and management of electric power system from the traditional vertical monopoly mode to transmission open access mode by splitting an original integrated system into three parts: generation, transmission, and distribution. While trying to introduce competitions and to optimize resource utilization, this reformation has brought a number of challenges to power system operation and planning, including the transmission costs distribution, network loss allocation, and congestion management. In the environment of deregulation and electricity market, it is extremely important to quickly and accurately determine the contributions of individual generators and loads to line flows, active power transfers between individual generators and loads, and distributions of power losses. Research on how to accurately determine the system usage of different market participants and fairly allocate the transmission costs and network losses among the market participants is of significant importance both in theory and in practice to mitigate transmission congestions and to assure a secure operation of the power systems.
Sponsored in part by the Chongqing Natural Science Foundation projects of“Research on power flow analysis theory and its application in electricity markets”and“Research on model and algorithm of transmission congestion management in electricity markets”, this thesis has completed a detailed study on the power flow tracing (PFT) technique and its application to transmission congestion management.
In order to overcome the shortcomings of existing PFT methods in published literatures so far, such as time-consuming search and tracing processes and requirement for a specific tracing principle, an effective and fast analytical tracing model and its solution algorithm for PFT were proposed. The construction approach of the down-stream distribution matrix (DSDM) and the properties of DSDM, such as a diagonally dominant and upper triangular matrix were discussed. The quantitative relationship of DSDM associated with the bus power injection, generation and load power vectors was derived. The concept of distribution coefficient matrix (DCM) of the generation bus to the load bus was presented and the analytical model of power distribution between generations and loads was built. The correctness of PFT algorithm based on the DSDM was shown using the matrix theory. This method was applied to the IEEE-RTS, NewEngland-39, and IEEE-118 power systems to demonstrate the power distribution among generators, loads and transmission lines. The case studies have shown promising application results of the proposed approach.
Usually, a power system can be equivalent to a lossless network for PFT studies as there are always power losses in power transmission lines. As we know, the current in power systems is lossless and its real and imaginary parts are orthogonal. Based on this property, an effective analytical model and algorithm for tracing current using extended incidence matrix (EIM) were introduced to improve the accuracy of power flow tracing and loss allocation. The concept and construction approach of EIM were presented. The properties of the EIM, such as the property of the sum of the row and column elements, were discussed. A network can be decomposed into two separate networks: the real and the imaginary current networks based on an AC power flow solution. The EIM corresponding to each current network can be also derived. Based on the generation injections and load current vectors resulted from the AC power flow solution, an analytical current tracing model between generators and loads can be established. More accurate results of PFT and loss allocation can be obtained from this current tracing model. The correctness of the current allocation and extraction can be proved using the basic electric network theorem. In other words, after current tracing, the currents injecting to a node are subjecting KCL and the voltages across branches satisfy the KVL. The major advantage of the proposed method is that the matrix theory is directly used without proportional sharing assumption on the flow distribution. The tests on a four bus power system and the IEEE-RTS power system indicated that the developed technique can be applied to any power system with or without loop flows.
The power or current tracing model described above is to analyze the power allocation and extraction under specific operating conditions. This model can not meet the requirement of the real-time operation of a power systems since the loads in a power system vary with time. To keep power balance in the system, the generation outputs are also changing with time. It is necessary to re-calculate the power flow tracing in a timely manner. However, this is very inefficient or impractical in the real-time operation environment. In order to avoid the repeated calculations of PFT, the rule of power distributions and extractions varying with the change of generation outputs was analyzed according to PFT or current tracing model. The curve of power flow tracing (CPFT) model was built based on the polynomial theory and was solved by using the least square method. The Taylor series theory was used to estimate the approximate solution of the dynamic PFT model. The PFT sensitivity was presented based on the CPFT model, which can be used to express the change of line flow varying with generation outputs. The congestion on a line can be eliminated efficiently by determining the generating units and the amounts of adjustment according to the PFT sensitivity and the overload of line flows. In turn, the congestion management can be realized by eliminating the line congestion one by one. The tests on the IEEE-RTS power system and other practical systems have shown correctness and effectiveness of the proposed method.
A non-linear regression model (NRM), which reflects the relationship between the results of PFT and generation outputs, was proposed according to a non-linear characteristic of power systems. The NRM was transformed to linear regression model by using the idea of transposition. The Monte Carlo method was used to simulate the examples based on PFT results. The NRM was solved by the least square method using the simulated examples. The relations between the disturbance of congested lines and that of generation outputs were obtained based on the Taylor series theory and the NRM, which are formulated to the equality constraints of the congestion management model (CMM). The CMM was formulated to minimize the total costs and was solved by using the Lagrange multiplier method. Tests on the IEEE-RTS power system and other practical systems show that the proposed method is effective.
本文受到重庆市自然科学基金“电力市场潮流分析的理论和应用研究”和“电力市场输电阻塞管理模型与算法研究”等相关课题的资助,对电力市场环境下潮流跟踪模型和算法以及基于潮流跟踪的输电阻塞管理等进行了深入研究。
针对已有功率跟踪方法需经过大量的搜索、跟踪或等值,需假设跟踪原则的不足,提出一种有效、快速的功率跟踪解析模型及求解算法。构造顺流分配矩阵并分析其对角占优、上三角等特点。建立该矩阵与节点注入功率矩阵、负荷功率矩阵以及发电机出力矩阵间的量化关系。提出发电机对负荷功率分配系数矩阵的概念,建立发电机对负荷功率分配、负荷对发电机功率汲取的解析模型。应用矩阵理论证明了基于顺流分配矩阵的功率跟踪算法的正确性。应用IEEE-RTS、NewEngland39和IEEE-118等测试系统,实现发电机、负荷以及线路间的功率分配,展示了良好的应用效果。
系统输送功率时总会在支路上产生损耗,而在进行功率跟踪时常需将实际有损网络等值为无损网络。为提高潮流跟踪和损耗分摊的准确度,根据电流具有无损的特点,提出一种基于扩展关联矩阵的电流跟踪解析模型及求解算法。给出节点间扩展关联矩阵的概念及构造方法,分析该矩阵行元素之和、列元素之和等优良性质。根据交流潮流结果将实际网络分解为实部和虚部电流网络并建立其对应的扩展关联矩阵。根据发电注入以及负荷电流矩阵计算电流跟踪分配系数矩阵,建立发电机对负荷电流分配的解析模型。基于电流跟踪模型进而得到潮流跟踪和损耗分摊的精确结果。论文用定理保证了电流分配和汲取的正确性,并采用电路理论证明跟踪前后节点电流和回路电压均能分别满足电力网络的KCL和KVL定律。该模型不需分摊原则的假设前提,而是通过矩阵分析直接解析求解,可用于无环流/环流网络。通过对测试系统的计算分析,证实了算法的有效性。
电力系统需时刻保持电力平衡,而电力负荷随时间在不断变化,致使电力系统的潮流以及潮流跟踪的结果也随时间变化。前述功率或电流跟踪模型是在给定运行方式下分析功率的分配和汲取情况,不能满足电力系统运行实时性要求。当发电机组出力或负荷变化时,常需重复进行潮流跟踪计算。为有效避免该重复计算,基于多项式理论和潮流跟踪原理建立了描述功率的汲取和分配随运行方式变化规律的潮流跟踪曲线模型。在系统各种运行方式下,分别应用前述功率和电流跟踪模型采集样本数据,进而运用最小二乘法求解潮流跟踪曲线模型。根据Taylor级数理论得到潮流跟踪动态计算的近似模型。在此基础上提出潮流跟踪灵敏度的概念,以描述机组出力变化对支路功率变化的影响程度。根据潮流跟踪灵敏度以及支路潮流越限量确定阻塞管理中参与调整的机组及其出力调整量,采用逐条支路消去法实现输电阻塞管理。对IEEE-30和IEEE-RTS系统进行潮流跟踪的近似计算以及从单回线路、不同位置线路和多条线路阻塞等角度进行输电阻塞管理分析计算,验证了该方法的有效性和正确性。
电力系统中,任意机组出力的变化都会影响潮流跟踪结果。基于此,结合潮流跟踪曲线的思想建立了反映支路潮流跟踪结果与机组出力间非线性关系的多元非线性回归模型。应用变换思想将非线性回归模型转化为线性回归模型,基于前述潮流跟踪模型和Monte Carlo模拟法产生机组出力和潮流跟踪样本,进而应用最小二乘法求解模型。为避免逐条支路消除法可能出现震荡的不足,采用同时消除法进行阻塞管理,根据多元非线性回归模型,基于Taylor级数得到所有阻塞线路潮流越限量与各机组出力调整量之间的关系,以此构成等式约束条件,从而建立以调整费用最小为目标的输电阻塞管理模型,并用拉格朗日乘子法进行求解。将该方法应用于IEEE-RTS等系统,对单回和多回线路阻塞以及不同线路阻塞等情况,以不同目标函数进行输电阻塞管理,验证了该方法的有效性和正确性。
The reformation of electric power industry has gradually changed the operation and management of electric power system from the traditional vertical monopoly mode to transmission open access mode by splitting an original integrated system into three parts: generation, transmission, and distribution. While trying to introduce competitions and to optimize resource utilization, this reformation has brought a number of challenges to power system operation and planning, including the transmission costs distribution, network loss allocation, and congestion management. In the environment of deregulation and electricity market, it is extremely important to quickly and accurately determine the contributions of individual generators and loads to line flows, active power transfers between individual generators and loads, and distributions of power losses. Research on how to accurately determine the system usage of different market participants and fairly allocate the transmission costs and network losses among the market participants is of significant importance both in theory and in practice to mitigate transmission congestions and to assure a secure operation of the power systems.
Sponsored in part by the Chongqing Natural Science Foundation projects of“Research on power flow analysis theory and its application in electricity markets”and“Research on model and algorithm of transmission congestion management in electricity markets”, this thesis has completed a detailed study on the power flow tracing (PFT) technique and its application to transmission congestion management.
In order to overcome the shortcomings of existing PFT methods in published literatures so far, such as time-consuming search and tracing processes and requirement for a specific tracing principle, an effective and fast analytical tracing model and its solution algorithm for PFT were proposed. The construction approach of the down-stream distribution matrix (DSDM) and the properties of DSDM, such as a diagonally dominant and upper triangular matrix were discussed. The quantitative relationship of DSDM associated with the bus power injection, generation and load power vectors was derived. The concept of distribution coefficient matrix (DCM) of the generation bus to the load bus was presented and the analytical model of power distribution between generations and loads was built. The correctness of PFT algorithm based on the DSDM was shown using the matrix theory. This method was applied to the IEEE-RTS, NewEngland-39, and IEEE-118 power systems to demonstrate the power distribution among generators, loads and transmission lines. The case studies have shown promising application results of the proposed approach.
Usually, a power system can be equivalent to a lossless network for PFT studies as there are always power losses in power transmission lines. As we know, the current in power systems is lossless and its real and imaginary parts are orthogonal. Based on this property, an effective analytical model and algorithm for tracing current using extended incidence matrix (EIM) were introduced to improve the accuracy of power flow tracing and loss allocation. The concept and construction approach of EIM were presented. The properties of the EIM, such as the property of the sum of the row and column elements, were discussed. A network can be decomposed into two separate networks: the real and the imaginary current networks based on an AC power flow solution. The EIM corresponding to each current network can be also derived. Based on the generation injections and load current vectors resulted from the AC power flow solution, an analytical current tracing model between generators and loads can be established. More accurate results of PFT and loss allocation can be obtained from this current tracing model. The correctness of the current allocation and extraction can be proved using the basic electric network theorem. In other words, after current tracing, the currents injecting to a node are subjecting KCL and the voltages across branches satisfy the KVL. The major advantage of the proposed method is that the matrix theory is directly used without proportional sharing assumption on the flow distribution. The tests on a four bus power system and the IEEE-RTS power system indicated that the developed technique can be applied to any power system with or without loop flows.
The power or current tracing model described above is to analyze the power allocation and extraction under specific operating conditions. This model can not meet the requirement of the real-time operation of a power systems since the loads in a power system vary with time. To keep power balance in the system, the generation outputs are also changing with time. It is necessary to re-calculate the power flow tracing in a timely manner. However, this is very inefficient or impractical in the real-time operation environment. In order to avoid the repeated calculations of PFT, the rule of power distributions and extractions varying with the change of generation outputs was analyzed according to PFT or current tracing model. The curve of power flow tracing (CPFT) model was built based on the polynomial theory and was solved by using the least square method. The Taylor series theory was used to estimate the approximate solution of the dynamic PFT model. The PFT sensitivity was presented based on the CPFT model, which can be used to express the change of line flow varying with generation outputs. The congestion on a line can be eliminated efficiently by determining the generating units and the amounts of adjustment according to the PFT sensitivity and the overload of line flows. In turn, the congestion management can be realized by eliminating the line congestion one by one. The tests on the IEEE-RTS power system and other practical systems have shown correctness and effectiveness of the proposed method.
A non-linear regression model (NRM), which reflects the relationship between the results of PFT and generation outputs, was proposed according to a non-linear characteristic of power systems. The NRM was transformed to linear regression model by using the idea of transposition. The Monte Carlo method was used to simulate the examples based on PFT results. The NRM was solved by the least square method using the simulated examples. The relations between the disturbance of congested lines and that of generation outputs were obtained based on the Taylor series theory and the NRM, which are formulated to the equality constraints of the congestion management model (CMM). The CMM was formulated to minimize the total costs and was solved by using the Lagrange multiplier method. Tests on the IEEE-RTS power system and other practical systems show that the proposed method is effective.
引文
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