Three-phase power flow calculations using the current injectionmethod

This paper presents a new sparse formulation for the solution of unbalanced three-phase power systems using the Newton-Raphson method. The three-phase current injection equations are written in rectangular coordinates resulting in an order 6n system of equations. The Jacobian matrix is composed of 6×6 block matrices and retains the same structure as the nodal admittance matrix. Practical distribution systems were used to test the method and to compare its robustness with that of the backward/forward sweep method     

基于直角坐标注入电流形式的多平衡节点潮流算法研究

对常规潮流计算中节点注入量由牛顿法的复功率改变为电流,修正方程中的不平衡量由计算有功和无功功率的偏差改变为计算节点注入电流偏差,对于PQ节点,雅克比矩阵只需修正对角块元素,简化了雅克比矩阵的变量元素。同时,针对常规潮流算法中功率不平衡量有一个平衡机承担问题,提出了一种处理多平衡节点的潮流算法,使功率不平衡量由多个发电单元分摊。该算法物理意义清晰,容易实现,收敛性好,给出的算例验证了提出算法的可行性。     

Voltage control devices models for distribution power flow analysis

This paper presents the development of mathematical models for thyristor controlled series compensator (TCSC), for voltage regulator devices and for remote bus voltage control that are suitable to be used with the three-phase current injection method (TCIM) for power flow calculation. TCIM is a Newton method where the equations are written in rectangular coordinates resulting in a 6n×6n Jacobian matrix. The representation of a control device requires an augmented system of equations to incorporate the additional relationship between each control action and the controlled variable, resulting in an augmented Jacobian matrix. Practical distribution systems are tested and the effectiveness of the proposed formulation is demonstrated     

A robust power flow model for active power flow control via thyristor‐controlled series compensator

In this paper, a new power flow model for active power flow control through a thyristor‐controlled series compensator (TCSC) in an AC network system is proposed. The proposed power flow model is based on the Newton–Raphson method. In this model, TCSC's admittance effect is included as a state variable into the Jacobian matrix to avoid the divergence problem. Unlike similar studies in the literature, TCSC's admittance is ignored in the bus admittance matrix, and the need for rebuilding the bus admittance matrix in each power flow iteration caused by the change of TCSC's admittance is prevented. So, faster convergence for power flow calculation is achieved. For this aim, new power equations are obtained. Also, in the proposed approach, we need not consider each terminal of TCSC as an individual bus in the power flow calculation. Thus, increasing the Jacobian and bus admittance matrixes sizes caused by the total bus number is prevented. The proposed approach is tested on an IEEE 57‐bus test system. The obtained results prove that this approach provides efficient, reliable, and fast convergence. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

以支路为基元的封闭格式潮流算法

针对潮流修正方程计算中新注入元处理繁琐的问题,以支路微增模型为基元,充分利用极坐标下牛顿潮流计算中因子分解过程、节点编号及稀疏存储三者间的关联,形成封闭格式的潮流算法。该算法采用支路微增模型的修正方程表达,并以追加形式与雅可比矩阵直接关联,无需导纳阵。依据节点编号同因子分解的关联性质,在节点编号的同时,跟踪未来与数值计算关联的拓扑结构,使前代自动定位,回代自动释放,形成封闭的计算格式,以期提高潮流计算算法的性能。以简单6节点电网为例详细阐述封闭计算格式的计算过程,通过3个IEEE标准系统算例,验证了所提方法在内存和计算速度上的优势。     

基于牛顿法的配电网络Zbus潮流计算方法

根据配电网的特点,在比较各类算法的基础上提出了一种新的基于牛顿法的配电网潮流算法。该算法从Zbus算法出发,对网络方程进行虚实部分解,形成的雅可比矩阵与节点导纳矩阵有极大的相似性,迭代中雅可比矩阵仅有少部分对角元素需要修改。算法通过修改雅可比矩阵元素来处理PV节点,还能够处理几种不同类型的负荷模型。理论分析和计算表明该算法性能优良,是配电网络潮流分析的有效方法。     

线路开断下牛顿潮流的补偿算法

利用补偿算法处理ＰＱ解耦潮流中的线路开断问题,获得了很大成功,原则上,补偿算法也能适用牛顿潮流解,但其具体实施方法迄今未见报导,文章提出了将补偿法用于线路开断下ＮＲ潮流的实施方案,并与重新形成线路开断后雅可比矩阵的牛顿银法在ＩＥＥＥ１４,３０以有５７节点算例系统上进行了数值试验和比较,结果说明了文章所述算法的正确性和可用性。     

Improved NR current injection load flow using power mismatch representation of PV bus

This letter presents improvement in the revised current injection mismatch load flow method (NR-RCIM) using new representation of voltage controlled bus (PV bus). In the proposed formulation, the representations of PV buses are based on power mismatches and the other PQ buses based on current mismatches. This combined power and current injection mismatches method (NR-PCIM) decreases the required current injection load flow equations and improves the convergence performance in case of PV buses. Tests and comparisons among different Newton Raphson load flow techniques: conventional Newton Raphson (NR), NR-RCIM and the new NR-PCIM have been held to illustrate the validity and merits of the proposed algorithm.     

A simple implementation of power mismatch STATCOM model into current injection Newton–Raphson power-flow method

This paper presents a simple implementation of Static Shunt Compensator (STATCOM) into Newton–Raphson current injection load flow method. The controlled STATCOM bus in the network is represented by voltage-controlled bus with zero active power generation at the required voltage magnitudes. The power mismatch equation of the connected STATCOM bus is included in Newton–Raphson current injection load flow algorithm, while the other PQ buses are represented by current mismatch equations. Moreover, the parameters of STATCOM can be calculated during iterative process and the final value will be updated after the convergence is achieved. This representation of generator buses reduces the number of required equations with respect to the classical and improved versions of the current injection methods. In addition of that the developed model reduces the complexities of the computer program codes and enhances the reusability by avoiding modifications in the Jacobian matrix. The performance of the developed STATCOM model has been tested using standard IEEE systems.     

Power flow control and solutions with multiple and multi-type FACTS devices

In this paper, a new generalized current injection model of the modified power system using Newton–Raphson power flow algorithm has been proposed for desired power transfer with Flexible AC Transmission Systems (FACTS) devices. So that the FACTS devices can be incorporated in the proposed algorithm and, therefore, whole system with these devices can be easily converted to power injection models without change of original admittance and the Jacobian matrices. Power flow algorithm has been modeled in such a way that it can easily be extended to multiple and multi-type FACTS devices by adding a new Jacobian corresponding to that new device only. Power flow algorithm with the presence of Thyristor Controlled Series Compensators (TCSC), Unified Power Flow Controller (UPFC), and Generalized Unified Power Flow Controller (GUPFC) has been formulated and solved. To demonstrate the performance of the proposed algorithm for multiple and multi-type FACTS devices, different case studies of IEEE 30-bus system has been considered and the results are tabulated. The proposed algorithm is independent of the size of the system and initial starting conditions of the FACTS devices.     

A Novel Power Flow Algorithm for Hybrid AC/DC Power Grids

This study introduces a novel unified power flow algorithm for hybrid AC/DC power grids. For hybrid AC/DC power grids that incorporate voltage source converters (VSCs), the proposed algorithm uses the voltage amplitude and the phase angle of the AC bus and the voltage of the DC bus as the minimum set of state variables. The power equation of the converter is deduced by these state variables. Then, the bus-power-equilibrium (BPE) equations can be deduced based on the DC node classification and VSC converter station control modes. The Newton–Raphson method can be used to solve these BPE equations with good convergence behavior. In addition, the DC grid and converter station modeling impose no restriction on the hybrid grid topology. As a result, the Jacobian matrix in the modified equations can accurately reflect the coupling relationship between AC and DC grids and simultaneously maintain the sparse feature. The proposed unified algorithm uses the sparse technology and can solve the power flow problem for a large hybrid power grid. A simulation is implemented to illustrate the effectiveness of the proposed algorithm.     

MODELING AND ELIMINATION OF LOAD BUSES IN OPTIMAL POWER FLOW SOLUTIONS

ABSTRACT

This paper presents a method to solve the optimal power flow problem after eliminating load buses from the system. Loads are first modeled and reflected in the admittance matrix and then their respective buses are eliminated. The obtained model is a reduced model of the original system. The admittance matrix is of the same order as the number of voltage-controlled buses in the system. The variables of the reduced model are the voltage-controlled buses voltages, angles and active power generations. Newton Raphson method is used to calculate the variables of the reduced model while minimizing an objective function. Voltages and angles of the original system are then calculated by a direct method. These voltages are required to update load models and to check for voltage and line current violations at the eliminated portions of the network. The simulation is carried out on two systems, IEEE 118 bus test system and a 131 bus actual system. It is shown that solution time is significantly reduced when compared to the conventional optimal power flow Newton Raphson method using the original system.     

Fast computation and stable convergence technique for unbalanced load flow calculation in large‐scale systems

This paper presents a new method of unbalanced load flow calculation to improve complexity by the method of advanced symmetrical coordinates. Usually, the electric power system has been calculated only by the positive phase sequence component on the assumption that three‐phase transmission lines and loads are balanced. However, many ultrahigh‐voltage transmission lines are not transposed, and therefore mutual inductances cause negative sequence currents in the trunk transmission system. Negative sequence currents cause heating of generators and transformers, and therefore the three‐phase sequence component should be calculated accurately. We examined the fast computation and good convergence performance of unbalanced load flow calculation by models of three‐phase transmission lines, transformers, and loads. The proposed method is not the phase coordinate system but the method of symmetrical coordinates. This technique decreases numerical complexity by the use of a simplified Jacobian matrix. The convergence performance of this method is inferior to that of the usual Newton–Raphson method. As a consequence, the problem of poor convergence performance is alleviated by a technique for the newly developed deceleration Newton method. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 174(1): 17–24, 2011; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21034     

基于松弛牛顿法的互联电网并行分布式潮流计算方法

分布式潮流计算是解决多区域互联电网一体化潮流问题的有效方法。以松弛牛顿法潮流求解公式为出发点,首先利用矩阵分裂法,将互联电网分解为相互独立的子系统,然后利用矩阵求逆运算的Sherman-Morrison-Woodbery公式对各子系统进行协调求解,从而导出了一种新的互联电网并行分布式潮流计算方法。与基于网络分解及协调计算的分布式潮流计算方法相比,该方法具有更好的收敛性。利用基于PVM的分布式计算环境,以IEEE118节点系统为例,对所提算法进行了装配、测试以及分析,初步验证了所提算法的有效性。     

A new formulation and solution method for the maximum loading point in electrical power systems

This paper proposes a new efficient formulation and solution method for a maximum loading point or saddle node bifurcation point in electrical power systems. This point, corresponding to a tip of the P(Q)-V curve, is characterized by singularity of the load flow Jacobian. The proposed formulation is of dimension n + 1, instead of 2n + 1 in the standard formulation, for n-dimensional load flow equations. The proposed method uses a 1-dimensional singularity condition, obtained from a reduction of the standard n + 1-dimensional singularity conditions. For this reduction, one of the diagonal elements of the load flow Jacobian is selected. We also propose an index for this selection to make the proposed method reliable. The solution for the proposed formulation can effectively be obtained based on the Newton-Raphson method with sparse matrix techniques. The computational performance of the proposed method is demonstrated on 6, 14, and 118 bus test systems. © 1997 Scripta Technica, Inc. Electr Eng Jpn, 121(1): 17–25, 1997     

A new sequential AC–DC power flow algorithm for multi‐terminal HVDC systems

This paper presents a new algorithm based on the sequential method for power flow calculation in integrated multi‐terminal, high‐voltage, direct current (HVDC) systems. Unlike similar studies in the literature, a real equivalent circuit model is considered for under‐load tap changer (ULTC) transformers of the DC converters, for the first time. So, new DC equations are obtained. Thus, exact and accurate results can be obtained for practical applications by the proposed algorithm. Adjustment effects of the DC converters' ULTCs tap values are included in the Jacobian matrix instead of the bus admittance matrix in the sequential AC power flow algorithm as well as other ULTCs in AC system. To this aim, new equations for the calculation of power and Jacobian matrix elements are obtained for the AC system. The proposed approach is tested on the modified IEEE 17‐bus AC–DC test system. Numerical results show that the proposed approach is accurate and reliable in convergence. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

电力系统直角坐标潮流二次方程新的表达型式

本文发展了电力系统潮流方程的一般表达型式，根据直角坐标形式下，潮流方程的特殊二次结构性质形成了潮流二次方程新的表达形式，并且给出了描述节点功率注入方程二次形式的Ｊ矩阵的结构和在这种亲折表达形式下的雅可比矩阵，为潮流计算提供了一种新的途径和解算方法。     

Augmented rectangular load flow model

This paper presents some improvements to the load flow solution in rectangular coordinates. First, in an attempt to use as linear a model as possible, both the nodal equations and the bus constraints are retained. The Newton-Raphson (NR) method is then applied to the enlarged set of equations, and written in terms of bus voltages and currents. This scheme, combined with a simple procedure to handle PV buses, leads to a computationally efficient algorithm, particularly advantageous in the presence of zero-injection buses. Experimental results are provided comparing the performance of the proposed approach with that of the conventional formulation     

基于预处理BICGSTAB法的电力系统潮流并行计算方法

为实现大规模电力系统潮流的准确、快速求解,以非精确牛顿法为基础,提出一种基于CPU-GPU异构平台的电力系统潮流并行计算方法。修正方程组的求解是牛拉法潮流计算中最为耗时的部分,提升修正方程组的求解效率可有效提升潮流计算效率。为此,根据雅可比矩阵的不对称不定性,采用稳定双正交共轭梯度(bi-conjugate gradient stabilized, BICGSTAB)法进行修正方程组的求解。进一步,为改善BICGSTAB法的收敛性,根据雅可比矩阵的稀疏性和类对角占优性,提出一种改进PPAT(Preconditioner with sparsity Pattern of AT, PPAT)预处理器和改进Jacobi预处理器相结合的两阶段预处理方法,并对雅可比矩阵进行预处理,提升BICGSTAB法的收敛性能。然后,将上述潮流算法移植到CPU-GPU异构平台,实现电力系统潮流的并行求解。最后,通过不同测试系统算例对所提方法进行验证、分析。结果表明,所提潮流并行计算方法可实现电力系统潮流的准确、快速求解。     

Power flow control for transmission networks with implicit modeling of static synchronous series compensator

This paper presents an implicit modeling of Static Synchronous Series Compensator (SSSC) in Newton–Raphson load flow method. The algorithm of load flow is based on the revised current injection formulation. The developed model of SSSC is depended on the current injection approach. In this model, the voltage source representation of SSSC is transformed to current source, and then this current is injected at the sending and auxiliary buses. These injected currents at the terminals of SSSC are a function of the required line flow and voltage of buses. These currents can be included easily to the original mismatches at the terminal buses of SSSC. The developed model can be used to control active and reactive line flow together or individually. The implicit modeling of SSSC device decreases the complexity of load flow code, the modification of Jacobian matrix is avoided, the change only will be in the mismatches vector. Finally, this modeling solves the problem that happens when the SSSC is only connected between two areas. Numerical examples on the WSCC 9-bus, IEEE 30-bus system, and IEEE 118-bus system are used to illustrate the feasibility of the developed SSSC model and performance of the Newton–Raphson current injection load flow algorithm.