A New Approach to Economic Dispatching Using Load Bus Elimination Techniques

This paper presents a new technique to solving the economic dispatch problem based on a reduced order model of the original system. Loads are first modeled by their appropriate voltage-dependent models as load admittances. Load admittances are then added to the bus admittance matrix and 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 voltagecontrolled buses in the system. The variables of the reduced model are the voltage-controlled buses’ angles and active power generations. Newton Raphson method is used to calculate the angles and active generations of the reduced model while minimizing the operational cost. Load bus voltages and angles of the original system are then calculated by a direct method and load admittances are modified. The process is repeated until convergence is achieved. The simulation is carried out on IEEE 118 bus test system. A comparison between the new approach and the penalty factors method has been made. It is shown that operational cost is improved and solution time is significantly reduced when compared to the penalty factors method of economic dispatch.     

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.     

Steady-state load shedding schemes: a performance comparison

This paper presents a formulation of the optimal steady-state load shedding problem that uses the sum of the squares of the difference between the connected active and reactive load and the supplied active and reactive power. The latter are treated as dependent variables modelled as functions of bus voltages only. The equality constraints associated with the power system load curtailment problem are the power flow equations in polar form utilizing the nodal admittance matrix approach. The inequality constraints are characterized by limits on line flows, voltage magnitudes and angles, and active and reactive power generations. The MINOS nonlinear optimization package is used to implement the optimization process. Testing is done using IEEE 14- and 30-bus power systems, and results obtained. The optimal results are compared with results obtained using two earlier approaches. The results obtained using the proposed approach appear to give a better optimal state of the power system.     

An enhanced RCGA for a rapid and reliable load flow solution of electrical power systems

The paper presents a reliable and fast load flow solution by using a real-coded genetic algorithm (RCGA), bus reduction technique and sparsity technique. The proposed load flow solution firstly used reduction technique to eliminate the load buses. Then, the power flow problem is solved for the generator buses only using real-coded GA to calculate the phase angles. Thus, the load flow problem becomes a single objective function, where the voltage magnitudes are specified resulted in reduced computation time for the solution. Once the phase angle has been calculated, the system is restored by calculating the voltages of the load buses in terms of the calculated voltages of the generator buses. A sparsity technique is used to reduce the computation time further as well as the storage requirements. The proposed load flow solution also can efficiently solve the load flow problems for ill-conditioned power systems whereas the conventional RCGA alone fails to solve these systems. The proposed method was demonstrated on 14-bus IEEE, 30-bus IEEE and 300-bus IEEE, and a practical system 362-busbar Iraqi National Grid. The proposed solution has reliable convergence, a highly accurate solution and much less computing time for on-line applications. The method can conveniently be applied for on-line analysis and planning studies of large power systems.     

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.     

方程求解法网络拓扑分析

具有多个电气岛的电力系统中,如果仅在某一个母线上加一个电源,则该母线所在电气岛内的所有母线电压都不为零,而其他电气岛中母线的电压则都为零,因此可以根据有无电压来判断电源点所在的电气岛。基于这一思想,提出了通过求解以邻接矩阵为系数矩阵的线性方程组进行网络拓扑分析的方法。该方法采用布尔运算形式的高斯消去法直接求解方程组,无需迭代。算法根据拓扑分析和布尔运算的特点简化了回代过程,并且根据消去后的系数矩阵特点设置右端向量,避免了前代过程。这些措施都有效地减少了计算量。同时可以利用各种求解稀疏方程组的技术手段有效地提高网络拓扑分析的速度。对一个实际大型电网进行了拓扑分析,计算结果表明了所提方法的正确性和有效性。     

辐射状配电网的逆流编号法

为了减少电力系统为导纳矩阵的运算量,节省计算机内存,人们提出了很多优化编号方法,但都不能保证节点导纳矩阵消去过程中不产生填充元为此,在深入分析配电风运行的辐射状结构特点的基础上,提出了一种新的节点优化法－－逆流编号法。其编号原则是：任一节点的编号必须大于其顺流节点的编号或任一节点的编号必须小于其逆流节点的编号。通过将逆流编号法与静态优化法进行比较可知,对于辐射型结构的配电网,逆流编号法总能保证节点     

Application of active power sensitivity to frequency and voltage variations on load shedding

The occurrence of a large disturbance in a power system can lead to a decline in the system frequency and bus voltages due to a real and reactive power deficiency or due to the formation of islands with generation–load imbalance. Load shedding is an emergency control action that can prevent a blackout in the power system by relieving the overload in some parts of the system. This paper shows that rate of change of frequency can be utilized to determine the magnitude of generation–load imbalance, while the rate of change of voltage with respect to active power can be utilized to identify the sensitive bus for load shedding. The frequency, voltages and their rate of change can be obtained by means of measurements in real-time from various devices such as digital recorders or phasor measurement units or these parameters can be estimated from the voltage data by other means such as an optimal estimation method like Kalman filtering. The rate of change of system frequency, along with the equivalent system inertia may be used to estimate the magnitude of the disturbance prior to each load shedding step. The buses with a higher rate of change of voltage may be identified as the critical ones for load shedding and load can be first shed at these buses, depending on the change in the power flow at each bus. This application is tested on the IEEE 30 bus system and the preliminary results demonstrate that it is feasible to be used in load shedding to restore system voltage and frequency.     

A new approach for evaluation of the bus admittance matrix from synchrophasors: (A statistical Ybus estimation approach)

In this research, a new parameter estimation technique for determining the bus admittance matrix (Ybus) is proposed to further calibrate power system models. Ybus estimation is done using recorded PMU synchrophasor measurements. The approach proposed in this research is based on recognizing that bus injection currents Ibus can be viewed as signals produced by a random process. In this manner, the corresponding bus voltages Vbus are also stochastic signals that are related through a cross-covariance matrix to the vector Ibus. Using estimation techniques developed for statistical signal processing, the cross-covariance matrix is shown to be Zbus. Research done previously in this area requires the prior knowledge of the electrical interconnection as well as full availability of PMU measurements. This method does not depend on prior knowledge of the electrical interconnection between the buses. It extracts the electrical interconnection and the parameters of the network model in the form of Ybus. It also does not require full availability of PMU measurements at each bus in the system. It estimates the partial Ybus based on the available PMUs.     

大规模电力系统分解聚合法直接暂态稳定分析

本文旨在研究用分解聚合网络方程解法进行大规模电力系统的直接暂态稳定分析．分析中网络用分块矩阵表示，故障所在子块发电机采用Ｅｑ恒定模型，负荷计及电压特性．而非故障子块则发电机采用经典模型、负荷作线性简化．能量函数计算采用ＰＥＢＳ法，并沿故障轨迹积分，以简化暂态能量的计算．通过对华中５７机３５５节点互联电力系统的大量计算及研究，证明了本文方法的快速性与实用性．     

电力系统潮流算法的几点改进

对电力系统传统潮流算法进行了如下几点改进：①提出了基于诺顿等值的多平衡节点处理方法。该方法既能解算具有多个平衡平点的同一电网潮流问题。也能够同时解算相互解列的、各自内部具有多个平衡节点的不同子网潮流问题。②针对小阻抗和零阻抗网络参数易导致节点导纳矩阵病态并影响潮流收敛速度和精度的同时,提出了基于节点等效附加注入的小阻抗和零阻抗处理方法。该方法可使节点导纳矩阵良性化,从而保证算法快速、准确地收敛。③针对PQ分解法的收剑性敏感于R/X比的问题,提出了基于节点等效附加注入的改进PQ分解法,使适用于高压输电系统的PQ分解法能够成功地应用于具有大R/X比的低压配电网潮流解算中。     

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.     

并联交流系统强度对换流母线电压稳定性的

随着中国互联电网的发展,交直流并联输电系统的电压稳定问题迫切需要研究。从并联交流系统强度出发,以四机两区域系统为例,利用负荷导纳模型算法求取节点电压稳定极限,然后采用负荷裕度和特征值分析方法,详细讨论了并联交流系统强度大小对逆变侧换流母线电压稳定性的影响。最后,利用电磁暂态仿真程序EMTDC／PSCAD对系统进行动态仿真,结果表明在重负荷备件下强并联交流系统有利于提高换流母线的电压稳定性。     

Real‐time calculation of power system bus voltage using a hybrid approach combining the Newton–Raphson method and dynamic programming

The calculation of the magnitudes and phase angles of the bus voltage is a challenging task in real‐time applications for power systems. Voltage profile, which denotes the present conditions of a power system, is determined by executing the traditional AC power flow program or by searching the supervisory control and data acquisition system. The AC power flow program is not suitable for several real‐time applications, such as contingency analysis and security control calculations, because of its complexity and convergence problems. Fast computation is the major concern in such applications. In this paper, a new method based on sensitivity factors, referred to as Jacobian‐based distribution factors (JBDFs), is proposed for calculating the magnitudes and phase angles of bus voltages. This method requires setting up JBDFs and deriving optimal solution paths of bus voltage for non‐swing buses through dynamic programming under base‐case loading conditions. Under real‐time conditions, the proposed method initially calculates real and reactive power line flows via JBDFs, and then computes the voltage magnitudes and phase angles of non‐swing buses through the derived optimal solution paths. The excellence of the proposed hybrid calculation method is verified by IEEE test systems. Simulation results demonstrate that the proposed method exhibits fast computation and high accuracy. Thus, the method is suitable for real‐time applications. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Dynamic Ward equivalents for transient stability analysis

In an effort to reduce the computing time of transient stability assessment, the paper presents a dynamic equivalent which results from the elimination of the load buses provided with voltage-dependent loads. The elimination is performed through a new version of the Ward equivalencing method. In this approach, the equivalent current injections are expressed in terms of the retained bus angles and a sensitivity matrix W_¯. The nonlinearity of the load flow model is accounted for through piecewise linear approximations by updating the W_¯ matrix whenever the operating point moves beyond the validity of the linearization. The paper also derives the expressions of the incremental changes in the generator electric power and the transient energy function for the reduced system. The approach has been tested on several systems with different sizes and characteristics     

On-line evaluation of loadability limit for pool model with TCSC using back propagation neural network

This paper presents an approach for on-line evaluation of loadability limit for pool model with Thyristor Controlled Series Compensator (TCSC) using Back Propagation Neural Network (BPNN). The optimal location, setting of TCSC and loadability limit for various load patterns in off-line are determined using Differential Evolution (DE) algorithm. This approach uses AC load flow equations with constraints on real and reactive power generations, transmission line flows, magnitude of bus voltages and TCSC setting. The input parameters to BPNN are real and reactive power loads at all buses. Data for training the BPNN is generated through Optimal Power Flow (OPF) solution using DE and the trained BPNN is tested with unseen load patterns. Sequential Forward Selection (SFS) belonging to greedy wrapper method is used for the selection of best optimal input features. Simulations are performed on 39 bus New England test system and IEEE 118 bus system. Solution accuracy and computation time are analyzed. The results obtained illustrate that, for on-line evaluation of loadability limit of pool model with TCSC, BPNN is accurate with minimal Mean Squared Error (MSE) and less computation time.     

Developments in the Newton Raphson power flow formulation based oncurrent injections

This paper describes a sparse Newton Raphson formulation for the solution of the power flow problem, comprising 2n current injection equations written in rectangular coordinates. The Jacobian matrix has the same structure as the (2n×2n) nodal admittance matrix, in which each network branch is represented by a (2×2) block. Except for PV buses, the off-diagonal (2×2) blocks of the proposed Jacobian equations are equal to those of the nodal admittance matrix. The results presented show that the proposed method leads to a substantially faster power flow solution, when compared to the conventional Newton Raphson formulation, expressed in terms of power mismatches and written in polar coordinates     

A parallel distributed computing framework for Newton–Raphson load flow analysis of large interconnected power systems

This paper proposes a simple parallel and distributed computing framework for the conventional Newton–Raphson load flow (NRLF) solution of large interconnected power systems. The proposed approach is based on message-passing distributed-memory architecture with separate workstations, and involves the piecewise analysis of power systems utilizing the network tearing procedure. The NRLF solution method, applied to each torn system at the selected buses, employs the matrix inversion lemma consisting of the factorization, forward elimination and back substitution procedures. The computational requirements of the state-of-the art parallel algorithm to obtain the correction vector involved in the back substitution procedure is reduced with the proposed approach in which the back substitution is carried out in parallel taking into account the split buses, rather than the order in which the forward elimination is performed. The investigations are carried out on the IEEE 118 bus standard test system in a Redhat Linux based 100 Mbps Ethernet LAN environment. The investigations reveal that the proposed method is significantly faster than the conventional NRLF and also the NRLF based on the state-of-the-art parallel algorithm, and thus finds potential applications for the real-time load flow solution of both regulated and deregulated power systems distributed over large geographical areas.     

输电网网损分摊方法的研究

提出了一种输电系统网损分摊方法，这种方法以网络稀疏的导纳矩阵为基础，指出在输电系统中进行功率交换者都应该是网损的承担者，各功率交换者应承担网损的份额与其在网络中的地点和交易量有关，将网损应合理分摊给功率交换者。这种方法与其他方法相比的突出优点是以潮流解为基础，容易理解和执行。它虽应用了网络等式但不需委任何假设，各功率交换者应承担网损的份额主委取决于网络导纳矩阵的实部及节点电压。给出了示例系统的计算结果并与其他方法的结果相比较，表明所提方法的合理性。     

电压稳定分析的潮流算法研究

研究了一种新型的用于电压稳定分析的潮流算法,它可充分考虑电力系统各种类型元件的模型,将常规潮流方程与动态元件的状态方程联立求解,同时解出系统中各个节点的电压、相角以及各种动态元件内部的状态变量。它考虑了系统中各种极限情况,消除了对于PV,PQ及平衡节点等的假设,使计算结果更加接近于系统的实际运行情况。采用上述潮流模型的连续潮流算法,对一个试验系统进行了电压稳定临界点的计算,并与常规潮流算法进行了比较。