Loss sensitivity formulas by adjoint networks

This paper presents a new set of formulas for computing power system loss sensitivities with respect to power system parameters. They are derived in the context of Tellegen's theorem and the concept of adjoint networks. The formulas are explicit, showing the combination of the power network quantities and the adjoint networks quantities. The formulas deal with branch-related and node-related parameters with equal ease. Data and numerical results for the adjoint quantities and for the sensitivities are presented.     

Security-constrained optimal rescheduling of real power usingHopfield neural network

A new method for security-constrained corrective rescheduling of real power using the Hopfield neural network is presented. The proposed method is based on solution of a set of differential equations obtained from transformation of an energy function. Results from this work are compared with the results from a method based on dual linear programming formulation of the optimal corrective rescheduling. The minimum deviations in real power generations and loads at buses are combined to form the objective function for optimization. Inclusion of inequality constraints on active line flow limits and equality constraint on real power generation load balance assures a solution representing a secure system. Transmission losses are also taken into account in the constraint function     

A generalized,complex adjoint approach to power network sensitivities

A unified study of the class of adjoint network approaches to power system sensitivity analysis which exploits the Jacobian matrix of the load flow solution is presented. Generalized sensitivity expressions which are easily derived, compactly described and effectively used for calculating first-order changes and gradients of functions of interest are obtained. These generalized sensitivity expressions are common to all modes of formulating the power flow equations, e.g. polar and Cartesian. the approach exploits a special complex notation and complex matrix manipulations to define the adjoint system and to derive the sensitivity formulae. the approach is applicable to both real and complex function sensitivities.     

考虑泵类负荷特性的低压配电网潮流计算

提出了一种考虑泵类负荷特性的低压配电网潮流计算方法。通过将泵类负荷的电动机转矩平衡方程和配电网各节点功率平衡方程组合起来,构成了考虑泵类负荷特性的低压配电网潮流计算模型。在求解配电网潮流计算的牛拉法的基础上,提出通过将泵类负荷电动机转矩平衡方程与各节点功率平衡方程进行统一迭代和交替迭代两种方法进行求解。通过对实际低压配电网台区的计算分析,验证了该方法能获得更加准确的配网负荷节点电压,而且能够获得泵类负荷正常运行时和启动时的节点电压。     

The multiple solution analysis of probabilistic load flow

The paper presents a new method of load flow calculation in which the known bus powers are treated as random variables. The probabilistic load flow equations are obtained from the quadratic deterministic load flow equations and are quartic. The deterministic equations have 2ⁿ⁻¹ solutions for n buses, and therefore the probabilistic equations should have at least the same number of solutions. The mathematical model is presented and the detailed equations for a two-bus power system are analysed. It is shown that the solutions of probabilistic load flow may be inadmissable if the random variables of the bus powers violate the boundary solution curve.The probabilistic load flow equations for power systems of general size are also derived. Results are exemplified for the Klos-Kerner three-bus and the Ward-Hale six-bus power systems.     

Z-bus loss allocation

This paper presents a new procedure for allocating transmission losses to generators and loads in the context of pools operated under a single marginal price derived from a merit-order approach. The procedure is based on the network Z-bus matrix, although all required computations exploit the sparse Y-bus matrix. One innovative feature and advantage of this method is that, unlike other proposed approaches, it exploits the full set of network equations and does not require any simplifying assumptions. The method is based on a solved load flow and is easily understood and implemented. The loss allocation process emphasizes current rather than power injections, an approach that is intuitively reasonable and leads to a natural separation of system losses among the network buses. Results illustrate the consistency of the new allocation process with expected results and with the performance of other methods     

含VSC-HVDC的交直流混合系统潮流统一迭代求解算法

介绍基于电压源换流器(VSC)的新一代高压直流输电(VSC-HVDC)技术,具有可向无源网络供电、不会出现换相失败等众多优点。分析VSC-HVDC输电系统的原理及其中VSC的控制方式。针对不同控制方式下的VSC,分别推导其交流母线及直流系统相应的潮流修正方程式。提出VSC-HVDC交直流混合系统潮流的统一迭代求解算法,并以修改后的WSCC-9节点交直流混合系统的潮流计算为例,验证统一迭代求解算法的有效性。通过该潮流算法分析VSC-HVDC输电系统的稳态特性和有功功率损耗特性。     

Adjoint network sensitivity based performance index evaluation for large-scale contingency events

This paper addresses the determination of power system performance indices based on the concept of adjoint networks and Tellegen's theorem. First-order sensitivities, as well as extensions to include expeditiously determinable higher order contributions, are dealt with. Derivations, algorithms, practical considerations, and numerical examples are presented. The relationship with state variable determination by adjoint network means is emphasized.     

Improvements in sparse matrix/vector technique applications foronline load flow calculation

Several analytical and computational improvements in sparsity applications are discussed. A novel partial matrix refactorization method and ordering algorithm are presented. The method is very efficient when applied to programs such as online load flow, optimal power flow, and steady-state security analysis. It is applied in a fast decoupled load flow program which includes the treatment of tap violations on underload tap changing transformers and reactive power generation on PV buses. The effects of proposed improvements are tested and documented on a 118-bus IEEE test network and two utility networks with 209 and 519 buses, respectively     

电力系统动态灵敏度计算的伴随方程方法

提出了计算电力系统动态灵敏度的一种新方法。针对电力系统的某一性能指标函数，构造了系统的伴随方程。伴随方程是一组与系统动态方程规模相同的微分代数方程组。通过求解一次伴随方程，即可计算该动态性能指标关于所有可调参数的动态灵敏度系数，因而其计算效率约为直接法的np倍(np倍为系统可调参数的个数)。同时，在求解伴随方程时采用了因子表重用技术，有效地提高了计算效率。采用该方法，只需在常规的暂态稳定分析计算之外附加很小的计算量，即可求得系统的动态灵敏度系数。文中讨论了与伴随方程方法相关的、动态系统的一些基本特性，以及伴随方程的构造方法，并且给出了伴随方程方法的算法流程和数值实例。     

Inherent structural characteristic indices of power system networks

Power equation relating an interconnected network is nonlinear and normally solved iteratively. This only gives numerical solution of a load flow without providing information on the structural relationship between buses that governs the solution that ensured. The absence of this information is an obstacle to readily solving most of power system problems. This paper seeks to overcome this limitation by proposing inherent structural indices that describe power system networks. These indices are obtained from the partitioned Y-admittance matrix based on circuit theory representation of networks. With these structural indices, an alternative method to determining the location of a new generator in a network is proposed and demonstrated.     

Effective techniques for reliability worth assessment in compositepower system networks using Monte Carlo simulation

Reliability cost/reliability worth assessment plays an important role in electric power system planning and operation. The paper proposes a technique for evaluating the costs of interruption and hence, the reliability worth in a composite power system network with time varying loads at load buses using sequential Monte Carlo simulation. A generalized methodology of determining the interruption costs, without considering the time varying aspect of the loads is discussed and the results are compared with those obtained by utilizing a load duration curve to represent the time dependent loads. Case studies conducted on the IEEE Reliability Test System (IEEE-RTS) are presented and discussed     

Power system voltage regulation based on voltage feedback using a dynamic capacitor

Over twenty-four hours of operation of a power system there is a wide variation in the demand, resulting in voltage fluctuation. This fluctuation may be large enough to lead to inefficient and unreliable operation of industrial plants. The fluctuation can be overcome by proper choice of controls (capacitors) located at suitable points on the power networks. To maintain the voltages within tight admissible limits, it is necessary to obtain a complete dynamic model of the generation-transmission system.In this paper, the dynamic model of a power system consisting of a synchronous generator, a transmission line containing four buses, and control capacitors placed at the buses is considered. Two types of control (capacitor) are used to regulate the voltages, (i) a synchronous capacitor and (ii) a static capacitor.A mathematical model of the controls is also presented. In this study, three separate cases of loads at the buses are simulated in the dynamic system. In all the cases the proposed controls are used to regulate the system voltages. The results indicate that, with the variation of loads, the desired voltage regulation can be achieved by proper choice of capacitor controls as functions of time.     

采用正规形方法确定重要负荷节点排序

电网结构是电力系统安全稳定运行的一个重要因素。为研究不同负荷节点对电压稳定性所具有的不同影响程度,首先应用向量场正规形理论分析电力系统潮流方程,提出了以节点电压非线性参与因子作为依据衡量负荷节点影响电压稳定性的程度的方法。该方法可计及电力系统非线性特性对电压稳定性的影响,因此与线性化分析方法相比,该方法在系统具有强非线性特性的条件下,仍能准确识别负荷节点的重要程度。然后用该方法研究了New England 39节点系统中不同负荷节点对电压稳定性的影响,通过对系统电压稳定性指标的比较,验证了所提出方法的有效性。     

一种少环配电网三相潮流计算新方法

针对少环配电网络的结构特点，提出了一种基于叠加原理求解少环配电网三相潮流的新方法。该方法首先将少环配电网络利用叠加原理分解为两个网络：不合环状结构的纯辐射状网络和不合辐射状结构的纯环状网络。然后对两个网络分别求解三相潮流，并将两个网络的计算结果叠加并迭代求解，最终求出整个网络的三相潮流。文中利用33节点系统进行了验算，并给出了验算结果；同时利用33节点系统、123节点系统和292节点系统进行了性能测试。结果表明，所提出的算法具有良好的收敛特性，能够有效地节约内存，具有很高的效率。     

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     

Power flow model/calculation for power systems with multiple FACTS controllers

This paper presents a new procedure for steady state power flow calculation of power systems with multiple flexible AC transmission system (FACTS) controllers. The focus of this paper is to show how the conventional power flow calculation method can systematically be modified to include multiple FACTS controllers. Newton–Raphson method of iterative solution is used for power flow equations in polar coordinate. The impacts of FACTS controllers on power flow is accommodated by adding new entries and modifying some existing entries in the linearized Jacobian equation of the same system with no FACTS controllers. Three major FACTS controllers (STATic synchronous COMpensator (STATCOM), static synchronous series compensator (SSSC), and unified power flow controller (UPFC)) are studied in this paper. STATCOM is modeled in voltage control mode. SSSC controls the active power of the link to which it is connected. The UPFC controls the active and the reactive power flow of the link while maintaining a constant voltage at one of the buses. The modeling approach presented in this paper is tested on the 9-bus western system coordinating council (WSCC) power system and implemented using MATLAB software package. The numerical results show the robust convergence of the presented procedure.     

An accurate voltage solution method for radial distribution systems

This paper formulates a set of equations (SOE) to describe a radial distribution system with high R/X ratio. The SOE comprises 3(N ? 1) second-order equations and an equal number of variables for an N-bus system. The proposed method solves this SOE using the first-order Newton-Raphson technique. The SOE model accounts for elements such as transformers, transmission lines, shunt capacitors, constant PQ loads, and constant impedance loads. Irrespective of the R/X ratio values of the lines in the system, the SOE preserves a strong diagonal characteristic. As well, this SOE is devoid of bus phase angles, unlike the 2(N ? 1) ac power flow equations used to describe transmission systems. The proposed method is compared with other methods reported in the literature for distribution systems, such as Newton-based methods and recursive methodologies that use forward and reverse sweeps. Tests conducted on radial distribution systems with 43, 69, and 5002 buses show the new method to be more accurate than other methods reported in the literature.     

A generalized power flow analysis for distribution systems with high penetration of distributed generation

In this paper, the element incidence matrix has been extended to develop a comprehensive three-phase distribution system power flow program for radial topology. Three-phase overhead or underground primary feeders and double-phase or single-phase line sections near the end of the feeder laterals have been considered. Unbalanced loads with different types including constant power, constant current and constant impedance are modeled at the system buses. Substation voltage regulator (SVR) consisting of three single phase units connected in wye or two single-phase units connected in open delta are modeled to satisfy the desired voltage level along the feeder. The mathematical model of distributed generation (DG) connected as PQ and PV buses are integrated into the power flow program to simulate the penetration of DGs in the distribution systems. The proposed method has been tested and compared with different IEEE test feeders result. The developed algorithm has been used to study the impact of both SVR and high penetration of DG on voltage profile and system power losses.