Reactive power transfer allocation method with the application of artificial neural network

A novel method to identify the reactive power transfer between generators and load using modified nodal equations is proposed. On the basis of the solved load flow results, the method partitions the Y-bus matrix to decompose the current of the load buses as a function of the generators' current and voltage. Then it uses the load voltages from the load flow results and decomposed load currents to determine reactive power contribution from each generator to loads. The validation of the proposed methodology is demonstrated by using a simple 3-bus system and the 25-bus equivalent system of south Malaysia. Next part here focuses on creating an appropriate artificial neural network (ANN) to solve the same problem in a simpler and faster manner. The basic idea is to use supervised learning paradigm to train the ANN. Most commonly used feedforward architecture has been chosen for the proposed ANN reactive power transfer allocation technique. Almost all system variables obtained from load flow solutions are utilised as an input to the neural network. Moreover, tan-sigmoid activation functions are incorporated in the hidden layer to realise the nonlinear nature of the reactive power transfer allocation. The targets of the ANN corresponding to the previously developed reactive power transfer allocation method. The 25-bus equivalent system of south Malaysia is utilised as a test system to illustrate the effectiveness of the ANN output compared with that of the modified nodal equations method. The ANN output provides promising results in terms of accuracy and computation time.     

Statistical Process Control

Collinearities can occur among the error-free (true) predictors in measurement-error models just as they occur among predictors in traditional regression models. The coefficient estimators for measurement-error models suffer the same ill effects of collinearities as do least squares estimators. For linear measurement-error models, collinearities are a property of the secondorder moment matrix of the unobservable error-free predictors. For nonlinear models, they are a property of the second-order moment matrix of derivatives of the nonlinear function. In this article, collinearities among the predictors in measurement-error models are defined, and diagnostics for their detection are discussed. The collinearity diagnostics introduced are similar to those used in traditional regression models, but they are applied to estimated second-order moment matrices of the error-free predictors rather than to the second-order moment matrix of the observed predictors. Examples are discussed, one of which demonstrates the masking of collinearities that can result from measurement errors.     

Assessment of MW-mile method for pricing transmission services: a negative flow-sharing approach

A negative flow-sharing approach to allocate transmission transaction charges among users of transmission services is proposed. The approach uses the properties of the MW-mile method but takes into account the economic benefits of both trading parties by analysing their shares in negative power flow or counterflow. This approach is incorporated with the justified distribution factor for power flow tracing purposes. Two case studies based on a 5-bus system and an IEEE 14-bus system are used to illustrate the proposed approach. The results show that the proposed approach has merit over the traditional MW-mile approaches in the context of revenue reconciliation of transmission services, regardless of transaction arrangements and locations. The profit-sharing concept introduced here provides a better economic signal in allocating charges for counterflows, which could benefit trading parties.     

Performance analysis of a novel q-limit guided continuation power flow method

This study presents a new bifurcation point calculation method that is based on the continuation power flow (CPF) method. The algorithmic continuation steps are guided by the prediction of Q-limit breaking points. A Lagrange polynomial interpolation formula is used in this study in order to find the Q-limit breaking point indices that determine when the reactive power output of a generator has reached its limits. The algorithmic continuation steps will then be guided to the closest Q-limit breaking point, consequently reducing the number of continuation steps and saving computational time. The novel method is compared with alternative conventional and enhanced CPF methods. Studies have been undertaken on IEEE 30, IEEE 118, National Grid (NG) 61 and NG 953 bus systems.     

High‐order predictor–corrector algorithms

New predictor–corrector algorithms are presented for the computation of solution paths of non‐linear partial differential equations. The predictors and the correctors are based on perturbation techniques and Padé approximants. This extends the Asymptotic Numerical Method (ANM), which is an efficient high‐order continuation technique without corrector. The efficiency and the reliability of the new technique are assessed by several examples within thin shell theory and Navier–Stokes equations. Many variants have been tested to establish an optimal algorithm. Copyright © 2002 John Wiley & Sons, Ltd.     

Transient stability constrained optimal power flow using particle swarm optimisation

A novel approach based on the particle swarm optimisation (PSO) technique is proposed for the transient-stability constrained optimal power flow (TSCOPF) problem. Optimal power flow (OPF) with transient-stability constraints considered is formulated as an extended OPF with additional rotor angle inequality constraints. For this nonlinear optimisation problem, the objective function is defined as minimising the total fuel cost of the system. The proposed PSO-based approach is demonstrated and compared with conventional OPF as well as a genetic algorithm based counterpart on the IEEE 30-bus system. Furthermore, the effectiveness of the PSO-based TSCOPF in handling multiple contingencies is illustrated using the New England 39-bus system. Test results show that the proposed approach is capable of obtaining higher quality solutions efficiently in the TSCOPF problem     

Reactive power/voltage control in distribution systems under uncertain environment

A novel method for reactive power/voltage control in distribution systems under uncertain data environment is presented. This is achieved by minimising boundary real power loss or boundary total real power demand while satisfying constraints on boundary bus voltage magnitudes. Such an approach is more realistic and intuitively satisfying as compared with the crisp solution with deterministic data assumption. On-load tap changing facility of the transformer at the substation and the shunt capacitors at the substation and feeders are used as control variables. A truly nonlinear fuzzy distribution power flow is used, in which simultaneous non-statistical uncertainties in load forecast, load model coefficients and network parameters are incorporated. Genetic algorithm is used to solve the problem. In order to demonstrate the effectiveness of the proposed method, results for balanced 30-bus and unbalanced 25-bus and modified 123-bus systems have been obtained.     

Power-current hybrid rectangular formulation for interior-point optimal power flow

A non-linear interior-point optimal power flow algorithm based on power?current hybrid mismatch formulation in rectangular coordinates is proposed. In the proposed algorithm, all buses are divided into two types: the buses with non-zero injections and the buses with zero injections. For the buses with non-zero injections, power flow equations are presented by power mismatch formulation. For the buses with zero injections, power flow equations are presented by current mismatch formulation. The proposed power?current hybrid formulation combines the advantages of both power mismatch and current mismatch formulations. For the buses with zero injections, the proposed hybrid formulation shares the advantages of current mismatch formulation: first-order derivatives of power flow equations become constants, second-order derivatives of power flow equations become zeros so that Jacobian and Hessian matrices of power flow equations are easier to compute. The hybrid mismatch formulation is also easier to handle the buses with non-zero injections than current mismatch formulation. Numerical studies on various testing systems indicate that the proposed hybrid formulation has better convergence performance and computational efficiency, especially for large-scale optical power flow problems with a large percentage of zero-injection buses.     

Solving multi-objective optimal power flow using differential evolution

A differential evolution approach to solve optimal power flow problem with multiple and competing objectives is presented. Two sub-problems of optimal power flow namely active power dispatch and reactive power dispatch are considered. The problem is formulated as a nonlinear constrained true multi-objective optimisation problem with competing objectives. Constrain-domination approach have been used to handle inequality constraints, which eliminates the use of penalty factors. The performance of the proposed approach was tested on standard IEEE 30-bus system and is compared with a conventional method. The result demonstrates the capability of the proposed approach to generate diverse and well-distributed Pareto-optimal solutions.     

梁杆结构二阶效应分析的一种新型梁单元

推导了一种计及梁杆二阶效应的新型两结点梁单元。首先依据插值理论构造了三结点Euler-Bernoulli梁单元的位移场:使用五次Hermite插值函数建立梁单元的侧向位移场,二次Lagrange插值函数建立梁单元的轴向位移场,进而由非线性有限元理论推导了单元的线性刚度矩阵和几何刚度矩阵,然后使用静力凝聚方法消除三结点梁单元中间结点的自由度,从而得到一种考虑轴力效应的新型两结点梁单元。实例分析表明,此新型梁单元具有很高的计算精度,使用此单元进行梁杆结构分析可获得相当准确的二阶位移和内力。     

改进的降阶牛顿迭代数值子结构方法

充分利用结构在地震作用下的局部非线性特征,数值子结构方法将原本复杂的结构非线性分析转化为以初始弹性刚度迭代的主结构等效线弹性分析和屈服构件隔离子结构非线性分析。由于主结构采用常刚度迭代分析收敛速度较慢,尚有一定局限性,于是该文提出一种改进的降阶牛顿迭代数值子结构方法。在主结构系统中,将塑性自由度位移场作为基本未知量,设计牛顿算法进行非线性迭代分析,并由隔离子结构跨平台非线性分析计算得到屈服单元的内力和切线刚度。对一平面15层3跨钢结构进行地震弹塑性时程分析,模拟结果表明：该文提出的方法是准确、可靠的,接近传统牛顿算法的二次收敛,且对于局部非线性结构系统,需要集成和分解的矩阵规模远小于传统方法。     

Robust design of multiple trailing edge flaps for helicopter vibration reduction: A multi-objective bat algorithm approach

The objective of this study is to determine an optimal trailing edge flap configuration and flap location to achieve minimum hub vibration levels and flap actuation power simultaneously. An aeroelastic analysis of a soft in-plane four-bladed rotor is performed in conjunction with optimal control. A second-order polynomial response surface based on an orthogonal array (OA) with 3-level design describes both the objectives adequately. Two new orthogonal arrays called MGB2P-OA and MGB4P-OA are proposed to generate nonlinear response surfaces with all interaction terms for two and four parameters, respectively. A multi-objective bat algorithm (MOBA) approach is used to obtain the optimal design point for the mutually conflicting objectives. MOBA is a recently developed nature-inspired metaheuristic optimization algorithm that is based on the echolocation behaviour of bats. It is found that MOBA inspired Pareto optimal trailing edge flap design reduces vibration levels by 73% and flap actuation power by 27% in comparison with the baseline design.     

Structure-preserved power-frequency slow dynamics simulation of interconnected ac/dc power systems with AGC consideration

A structure-preserved power-frequency slow dynamics simulation model is suggested for interconnected ac/dc power systems with automatic generation control (AGC) consideration, which will be applied to study relevant emergency control in future so that the bulk system viability crisis caused by load-frequency slow dynamics can be released. In the model, the network structure of interconnected power systems is entirely preserved, and the multi-area dynamic load flow (DLF) is developed for simulation. The generator speed governor and rotor dynamics, load-frequency characteristics, simplified models for high voltage direct current (HVDC) transmission and flexible ac transmission systems (FACTS) device thyristor controlled series capacitor (TCSC) suitable for long-term dynamics are considered with their AGC interfaces kept for future emergency-AGC study. However, at this stage, the sub-problem of reactive power and voltage is neglected for modelling simplicity and dc load flow is thus used for network solution. The concept of area centre of inertia (ACOI) is used based on the assumption of uniform frequency in each control area similar to that of the conventional single-area DLF calculation. The application of ACOI concept is attractive because the signal can be obtained from wide-area measurement systems (WAMSs) in real time and used to enhance long-term frequency stability through advanced control in future. The computer test results from 2-area 4-machine and IEEE 30-bus power systems demonstrated the validity and effectiveness of the suggested model and corresponding algorithm.     

Driving speed and the risk of road crashes: a review

Driving speed is an important factor in road safety. Speed not only affects the severity of a crash, but is also related to the risk of being involved in a crash. This paper discusses the most important empirical studies into speed and crash rate with an emphasis on the more recent studies. The majority of these studies looked at absolute speed, either at individual vehicle level or at road section level. Respectively, they found evidence for an exponential function and a power function between speed and crash rate. Both types of studies found evidence that crash rate increases faster with an increase in speed on minor roads than on major roads. At a more detailed level, lane width, junction density, and traffic flow were found to interact with the speed-crash rate relation. Other studies looked at speed dispersion and found evidence that this is also an important factor in determining crash rate. Larger differences in speed between vehicles are related to a higher crash rate. Without exception, a vehicle that moved (much) faster than other traffic around it, had a higher crash rate. With regard to the rate of a (much) slower moving vehicle, the evidence is inconclusive.     

A modified Newton‐type Koiter‐Newton method for tracing the geometrically nonlinear response of structures

The Koiter‐Newton (KN) method is a combination of local multimode polynomial approximations inspired by Koiter's initial postbuckling theory and global corrections using the standard Newton method. In the original formulation, the local polynomial approximation, called a reduced‐order model, is used to make significantly more accurate predictions compared to the standard linear prediction used in conjunction with Newton method. The correction to the exact equilibrium path relied exclusively on Newton‐Raphson method using the full model. In this paper, we proposed a modified Newton‐type KN method to trace the geometrically nonlinear response of structures. The developed predictor‐corrector strategy is applied to each predicted solution of the reduced‐order model. The reduced‐order model can be used also in the correction phase, and the exact full nonlinear model is applied only to calculate force residuals. Remainder terms in both the displacement expansion and the reduced‐order model are well considered and constantly updated during correction. The same augmented finite element model system is used for both the construction of the reduced‐order model and the iterations for correction. Hence, the developed method can be seen as a particular modified Newton method with a constant iteration matrix over the single KN step. This significantly reduces the computational cost of the method. As a side product, the method has better error control, leading to more robust step size adaptation strategies. Numerical results demonstrate the effectiveness of the method in treating nonlinear buckling problems.     

Second-order hot image from a scatterer in high-power laser systems

A theory is developed for predicting a second-order hot-image formation in high-power laser systems. Light diffracted from a small optical scatterer interferes with an intense original wave in the nonlinear medium to produce a hologram like a Fresnel-zone plate. The theoretical model shows that the hologram produces a negative first-order diffractive wave focused to the traditional hot image and negative second-order diffraction that causes another intense image, namely, a second-order hot image. It is found by analysis that the location of the second-order hot image arises in a downstream plane with a half-distance from the medium to the scatterer. Results of the numerical calculations show that the peak intensity of the nonlinear image may reach a level high enough to damage optical components with the increase of the breakup integral (B integral), indicating that the image may also potentially damage expensive optical components in high-power laser systems.     

Hybrid algorithm of differential evolution and evolutionary programming for optimal reactive power flow

Differential evolution (DE) is a promising evolutionary algorithm for solving the optimal reactive power flow (ORPF) problem, but it requires relatively large population size to avoid premature convergence, which will increase the computational time. On the other hand, evolutionary programming (EP) has been proved to have good global search ability. Exploiting this complementary feature, a hybrid algorithm of DE and EP, denoted as DEEP, is proposed in this study to reduce the required population size. The hybridisation is designed as a novel primary-auxiliary model to minimise the additional computational cost. The effectiveness of DEEP is verified by the serial simulations on the IEEE 14-, 30-, 57-bus system test cases and the parallel simulations on the IEEE 118-bus system test case.     

Stabilized finite element methods for vertically averaged multiphase flow for carbon sequestration

A computationally efficient numerical model that describes carbon sequestration in deep saline aquifers is presented. The model is based on the multiphase flow and vertically averaged mass balance equations, requiring the solution of two partial differential equations – a pressure equation and a saturation equation. The saturation equation is a nonlinear advective equation for which the application of Galerkin finite element method (FEM) can lead to non‐physical oscillations in the solution. In this article, we extend three stabilized FEM formulations, which were developed for uncoupled systems, to the governing nonlinear coupled PDEs. The methods developed are based on the streamline upwind, the streamline upwind/Petrov–Galerkin and the least squares FEM. Two sequential solution schemes are developed: a single step and a predictor–corrector. The range of Courant numbers yielding smooth and oscillation‐free solutions is investigated for each method. The useful range of Courant numbers found depends upon both the sequential scheme (single step vs predictor–corrector) and also the time integration method used (forward Euler, backward Euler or Crank–Nicolson). For complex problems such as when two plumes meet, only the SU stabilization with an amplified stabilization parameter gives satisfactory results when large time steps are used. Copyright © 2016 John Wiley & Sons, Ltd.     

剪切压电陶瓷块微位移测量及非线性修正

通过搭建的剪切压电陶瓷块微位移测量系统,进行了5个不同目标电压的剪切压电陶瓷微位移测量实验,对实验数据分别进行二阶、三阶、四阶最小二乘拟合后进行非线性修正实验,其中采用三阶最小二乘拟合进行修正时效果最好,其位移1 050 nm行程时最大非线性误差为3 nm。对所得三阶最小二乘拟合多项式的系数进行样条插值拟合,从而实现对不同目标位移的非线性修正,其中位移900 nm行程时最大非线性误差为4 nm,仅为原始非线性误差的11%。