输配电网潮流与优化的理论研究
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摘要
环境恶化、不可再生能源枯竭,驱使节能减排、能源洁净迫在眉睫。电能转换在能源利用中占主导地位,电力系统在电源构成上必将发生巨大变化。在这一背景下,输电、配电逐渐向不清晰、分散化、分布式方向发展。由此,电力系统潮流、优化潮流的理论面临新问题,对其进行深入研究有重要的理论意义和工程价值。
对此,在前人研究成果的基础上,本文从输配电网的潮流、优化潮流必须以全局理念进行分析的思想出发,深入研究了这一复杂问题,以潮流为核心,就各子问题、以及子问题间的分解与协调,展开理论与实践的探索,取得预期的成效,其主要创新性成果如下：
(1)针对交流电网潮流算法中不同稀疏存储格式下元素检索或注入元插入操作繁琐的问题,提出了极坐标下牛顿潮流数值计算过程、节点编号及稀疏处理相关联的封闭格式潮流算法。该算法以交流输电支路为基元,支路潮流微增模型直接关联雅克比矩阵,支路节点号定位待更新元素位置,避开了导纳阵的形成；利用节点编号与前代回代计算的关联,以拓扑形式显现消元过程中因子表结构变动,预测注入元并准确定位,使注入元插入操作简捷；采用三角检索存储格式,前代自动定位,回代自动释放,降低了信息检索的消耗。
(2)针对直流输电支路对交流电网潮流算法格式及收敛性的影响,提出直流输电支路等效为基元的交直流电网潮流算法。引入直流输电支路等效基元的概念,依据直流输电支路不同运行模式在数学上的相通性,将不同运行模式转化为一种等效模式,实现对直流输电支路基元模型的统一表达。在潮流计算中考虑直流输电支路时,仅需在交流网络修正方程基础上,追加其等效基元微增模型即可,对稀疏存储结构和计算格式无影响,从而使算法统一且有固定规律,交流输电支路为基元的潮流算法得以继续沿用。
(3)针对含大量分布式电源的输配电网潮流计算问题。首先分析其输、配电网间相互渗透的特点,表现在：有功方面,配电要么显现受端特性,要么显现电源特性；无功方面,要么输电依然支撑配电,要么配电也可能有其电压支撑的主动性；有功与无功间,要么依然处于弱耦合状态,要么出现紧密耦合状态。对上述表现的后者,体现出实施输配电网统一分析的必要性。在此基础上,在有功、无功平衡允许的约束条件下,以输电网为主问题和若干配电网为子问题,建立反映配电网与输电网间关联的潮流计算模型,提出以输配分界点电压为协变量的输配电网潮流的分解协调算法,同时计及相关信息的协调。实践表明,该算法简捷有效,在可行条件下有良好的收敛性,可满足输配电网联合计算的要求。
(4)就含分布式电源(风、光、储)的配电网,由于显现其主动行为,提出动态优化的模型,并予以机理分析。由于风、光、储共存的配电网中,不仅体现有功、无功及电压间的相互关联和耦合,而且因储能使一定周期内存在显著的时间关联,使配网潮流必须以动态优化方可挖掘其效能。在此基础上,详细阐述各类分布式电源特性及约束条件,从而建立相应的动态优化数学模型,并给出相应的求解方法。分析表明,该模型能有效发挥各类分布式电源的调节能力,实现资源的优化配置。
(5)针对分布式电源占相当比例的输配电网优化问题,提出必须实施输、配统筹的全网优化,并对输、配电间的作用机理予以分析。首先通过输、配电网边界节点变量复制,对输、配电网的变量、约束、目标函数进行分解,针对边界节点变量等式约束导致的优化问题不可分性,借助辅助问题原理,将其对应的增广拉格朗日函数转化为一系列可并行处理的辅助问题,从而以输、配电网优化子问题为基础,建立了二者相协调的输配电网优化潮流模型。该协调机制下,输、配电网只需关注其各自的优化子问题,通过交换少量边界信息对其边界节点上虚拟机组的成本参数进行修正,即可实现分区间的协调,达到输电、配电间资源的优化配置。实践表明,该算法实施便捷,收敛性好,对未来输配电网协调优化有理论储备和指导意义。
With the environment deterioration and non-renewable energy exhaustion, applying the energy conservation policy and making good use of clean energy are becoming extremely urgent. Electrical energy conversion is dominant in the use of energy, while the energy source composition in the power system will surely be significantly changed. In this context, electrical power transmission and distribution is about to develop gradually in an indeterminate, decentralized and distributed way. As a result, the theory of power flow and optimal power flow are facing new problems. It is theoretically significant and practically valuable to do its intensive study.
Based on the results of previous studies, the author of this thesis has done some depth-study of the complex issues mentioned above with the idea that the power flow in the transmission and distribution network and its optimization must employ the global analysis concept. Moreover, with the power flow as the core issue, this thesis expands the exploration of the theory and practice in the decomposition and coordination between each sub-problem and as well as each sub-problem itself and the expected results has been achieved. The main innovative results are as following:
1. To reduce the trouble in coping with newly added elements and element retrievals in different sparse storage format during the calculation of AC power flow correction equations, a closed format power flow algorithm is proposed, utilizing the incidence among the factorization process, the numbering of nodes and the sparse storage during Newton power flow calculation in polar coordinates. The proposed algorithm is expressed by correction equations of branch increment models and directly related to Jacobian matrix in additional form, so the element to be updated is located by branch node number and admittance matrix is not needed. According to the incidence between node numbers and forward-backward substitution operation, changes of factorization table structure in elimination process are described with the network topology changes, so that the newly added elements could be predicted and their operation would be easier to be made. Besides that, this algorithm uses triangle retrieve storage format and make automatic location of forward substitution operation and automatic releasing of backward operation, so that the consumption of retrieval information in the process of calculation is smart redued.
2. In allusion to the influence of DC transmission lines on the format and convergence of AC power flow calculation, a power flow algorithm for AC-DC power grid based on the equivalence elements of DC transmission line is proposed. According to the communication among different operation modes of DC transmission lines in mathematics, this algorithm translates various modes into one equivalent mode by introducing the concept of the equivalence modes of DC transmission line, in order to realize the unification of DC transmission line models. When considering DC transmission line in power flow calculation, this algorithm only need to add the incremental model of its equivalent model, so that sparse storage structure and computational format are not changed which means that the algorithm has unified and fixed rules and AC power flow algorithm based on AC transmission line modes can be continue used.
3. For the power flow calculation problem of power transmission-distribution network containing numerous distributed generations. Analysis about the interpenetration characteristics between transmission and distribution network is given. The characteristics are:in the active power aspect, the distribution network shows either the characteristics of receiving end or the power source part; in the reactive power aspect, either transmission grid will support the distribution network or the distribution network may show its voltage support initiative; in between, the active and the reactive power may be either weakly coupled or in strongly coupled state. Each of the latter part of the characteristics mentioned above demonstrates the necessity of the implementation of a unified analysis of the transmission and distribution network. On this basis, under the active and reactive power balance constraints, taking the transmission grid as the main problem and some distribution network as the sub-problem, power flow calculation model which displays the correlation between distribution grid and transmission grid is created. And at the same time, transmission and distribution network power flow decomposition and coordination algorithm with cut-off point voltage as covariant is proposed. In practice, it shows that the algorithm is simple and effective. Besides, under feasible conditions, the algorithm is with great convergence, which could satisfy the requirements of the computation of the transmission and distribution network.
4. For distribution networks including wind power, solar power and energy storage, the dynamic optimal power flow model is proposed and its mechanism is analyzed in order to describe the active behavior of distributed generations. Due to the coupling between real and reactive power and the connection in time, distribution network power flow need to be dynamicly optimized so that its efficiency can be fully expressed. On this basis, this thesis describes in detail the characteristics and constraints of different kinds of distributed generations, and proposes the corresponding dynamic optimal power flow model and its solution strategy. Numerical examples show that this model can fully utilize the regulation capability of distributed generations and realize the optimal configuration of power sources.
5. In allusion to the transmission-distribution network optimization problem with extensive distributed generations, this thesis proposes a whole network optimal power flow model and studies the effect rule between transmission and distribution network. Firstly, objective function, constraints and variables of transmission and distribution networks are decomposed with the replication of boundary variables. In allusion to the inseparability caused by equality constraints of boundary variables, auxiliary problem principle is applied and the augmented Lagrangian function is transformed into a series of auxiliary problems that can be solved in parallel, so that the coordinated transmission-distribution network optimal power flow model is proposed on the basis of transmission and distribution optimization sub-problems. Under that coordination mechanism, the two networks only need to treat with its own sub-problem and virtual generators costing parameters can be corrected with a little amount of boundary information exchange in order to realize the coordination of different areas and the optimal configuration of power sources. Numerical examples show that this algorithm is simple in computer implementation and has good convergence; therefore, it can be very useful theoretical reserve and of great guiding significance for coordinated transmission-distribution network optimal problems in the future.
对此,在前人研究成果的基础上,本文从输配电网的潮流、优化潮流必须以全局理念进行分析的思想出发,深入研究了这一复杂问题,以潮流为核心,就各子问题、以及子问题间的分解与协调,展开理论与实践的探索,取得预期的成效,其主要创新性成果如下：
(1)针对交流电网潮流算法中不同稀疏存储格式下元素检索或注入元插入操作繁琐的问题,提出了极坐标下牛顿潮流数值计算过程、节点编号及稀疏处理相关联的封闭格式潮流算法。该算法以交流输电支路为基元,支路潮流微增模型直接关联雅克比矩阵,支路节点号定位待更新元素位置,避开了导纳阵的形成；利用节点编号与前代回代计算的关联,以拓扑形式显现消元过程中因子表结构变动,预测注入元并准确定位,使注入元插入操作简捷；采用三角检索存储格式,前代自动定位,回代自动释放,降低了信息检索的消耗。
(2)针对直流输电支路对交流电网潮流算法格式及收敛性的影响,提出直流输电支路等效为基元的交直流电网潮流算法。引入直流输电支路等效基元的概念,依据直流输电支路不同运行模式在数学上的相通性,将不同运行模式转化为一种等效模式,实现对直流输电支路基元模型的统一表达。在潮流计算中考虑直流输电支路时,仅需在交流网络修正方程基础上,追加其等效基元微增模型即可,对稀疏存储结构和计算格式无影响,从而使算法统一且有固定规律,交流输电支路为基元的潮流算法得以继续沿用。
(3)针对含大量分布式电源的输配电网潮流计算问题。首先分析其输、配电网间相互渗透的特点,表现在：有功方面,配电要么显现受端特性,要么显现电源特性；无功方面,要么输电依然支撑配电,要么配电也可能有其电压支撑的主动性；有功与无功间,要么依然处于弱耦合状态,要么出现紧密耦合状态。对上述表现的后者,体现出实施输配电网统一分析的必要性。在此基础上,在有功、无功平衡允许的约束条件下,以输电网为主问题和若干配电网为子问题,建立反映配电网与输电网间关联的潮流计算模型,提出以输配分界点电压为协变量的输配电网潮流的分解协调算法,同时计及相关信息的协调。实践表明,该算法简捷有效,在可行条件下有良好的收敛性,可满足输配电网联合计算的要求。
(4)就含分布式电源(风、光、储)的配电网,由于显现其主动行为,提出动态优化的模型,并予以机理分析。由于风、光、储共存的配电网中,不仅体现有功、无功及电压间的相互关联和耦合,而且因储能使一定周期内存在显著的时间关联,使配网潮流必须以动态优化方可挖掘其效能。在此基础上,详细阐述各类分布式电源特性及约束条件,从而建立相应的动态优化数学模型,并给出相应的求解方法。分析表明,该模型能有效发挥各类分布式电源的调节能力,实现资源的优化配置。
(5)针对分布式电源占相当比例的输配电网优化问题,提出必须实施输、配统筹的全网优化,并对输、配电间的作用机理予以分析。首先通过输、配电网边界节点变量复制,对输、配电网的变量、约束、目标函数进行分解,针对边界节点变量等式约束导致的优化问题不可分性,借助辅助问题原理,将其对应的增广拉格朗日函数转化为一系列可并行处理的辅助问题,从而以输、配电网优化子问题为基础,建立了二者相协调的输配电网优化潮流模型。该协调机制下,输、配电网只需关注其各自的优化子问题,通过交换少量边界信息对其边界节点上虚拟机组的成本参数进行修正,即可实现分区间的协调,达到输电、配电间资源的优化配置。实践表明,该算法实施便捷,收敛性好,对未来输配电网协调优化有理论储备和指导意义。
With the environment deterioration and non-renewable energy exhaustion, applying the energy conservation policy and making good use of clean energy are becoming extremely urgent. Electrical energy conversion is dominant in the use of energy, while the energy source composition in the power system will surely be significantly changed. In this context, electrical power transmission and distribution is about to develop gradually in an indeterminate, decentralized and distributed way. As a result, the theory of power flow and optimal power flow are facing new problems. It is theoretically significant and practically valuable to do its intensive study.
Based on the results of previous studies, the author of this thesis has done some depth-study of the complex issues mentioned above with the idea that the power flow in the transmission and distribution network and its optimization must employ the global analysis concept. Moreover, with the power flow as the core issue, this thesis expands the exploration of the theory and practice in the decomposition and coordination between each sub-problem and as well as each sub-problem itself and the expected results has been achieved. The main innovative results are as following:
1. To reduce the trouble in coping with newly added elements and element retrievals in different sparse storage format during the calculation of AC power flow correction equations, a closed format power flow algorithm is proposed, utilizing the incidence among the factorization process, the numbering of nodes and the sparse storage during Newton power flow calculation in polar coordinates. The proposed algorithm is expressed by correction equations of branch increment models and directly related to Jacobian matrix in additional form, so the element to be updated is located by branch node number and admittance matrix is not needed. According to the incidence between node numbers and forward-backward substitution operation, changes of factorization table structure in elimination process are described with the network topology changes, so that the newly added elements could be predicted and their operation would be easier to be made. Besides that, this algorithm uses triangle retrieve storage format and make automatic location of forward substitution operation and automatic releasing of backward operation, so that the consumption of retrieval information in the process of calculation is smart redued.
2. In allusion to the influence of DC transmission lines on the format and convergence of AC power flow calculation, a power flow algorithm for AC-DC power grid based on the equivalence elements of DC transmission line is proposed. According to the communication among different operation modes of DC transmission lines in mathematics, this algorithm translates various modes into one equivalent mode by introducing the concept of the equivalence modes of DC transmission line, in order to realize the unification of DC transmission line models. When considering DC transmission line in power flow calculation, this algorithm only need to add the incremental model of its equivalent model, so that sparse storage structure and computational format are not changed which means that the algorithm has unified and fixed rules and AC power flow algorithm based on AC transmission line modes can be continue used.
3. For the power flow calculation problem of power transmission-distribution network containing numerous distributed generations. Analysis about the interpenetration characteristics between transmission and distribution network is given. The characteristics are:in the active power aspect, the distribution network shows either the characteristics of receiving end or the power source part; in the reactive power aspect, either transmission grid will support the distribution network or the distribution network may show its voltage support initiative; in between, the active and the reactive power may be either weakly coupled or in strongly coupled state. Each of the latter part of the characteristics mentioned above demonstrates the necessity of the implementation of a unified analysis of the transmission and distribution network. On this basis, under the active and reactive power balance constraints, taking the transmission grid as the main problem and some distribution network as the sub-problem, power flow calculation model which displays the correlation between distribution grid and transmission grid is created. And at the same time, transmission and distribution network power flow decomposition and coordination algorithm with cut-off point voltage as covariant is proposed. In practice, it shows that the algorithm is simple and effective. Besides, under feasible conditions, the algorithm is with great convergence, which could satisfy the requirements of the computation of the transmission and distribution network.
4. For distribution networks including wind power, solar power and energy storage, the dynamic optimal power flow model is proposed and its mechanism is analyzed in order to describe the active behavior of distributed generations. Due to the coupling between real and reactive power and the connection in time, distribution network power flow need to be dynamicly optimized so that its efficiency can be fully expressed. On this basis, this thesis describes in detail the characteristics and constraints of different kinds of distributed generations, and proposes the corresponding dynamic optimal power flow model and its solution strategy. Numerical examples show that this model can fully utilize the regulation capability of distributed generations and realize the optimal configuration of power sources.
5. In allusion to the transmission-distribution network optimization problem with extensive distributed generations, this thesis proposes a whole network optimal power flow model and studies the effect rule between transmission and distribution network. Firstly, objective function, constraints and variables of transmission and distribution networks are decomposed with the replication of boundary variables. In allusion to the inseparability caused by equality constraints of boundary variables, auxiliary problem principle is applied and the augmented Lagrangian function is transformed into a series of auxiliary problems that can be solved in parallel, so that the coordinated transmission-distribution network optimal power flow model is proposed on the basis of transmission and distribution optimization sub-problems. Under that coordination mechanism, the two networks only need to treat with its own sub-problem and virtual generators costing parameters can be corrected with a little amount of boundary information exchange in order to realize the coordination of different areas and the optimal configuration of power sources. Numerical examples show that this algorithm is simple in computer implementation and has good convergence; therefore, it can be very useful theoretical reserve and of great guiding significance for coordinated transmission-distribution network optimal problems in the future.
引文
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