A novel method for optimal capacitor placement and sizing in distribution systems with nonlinear loads and DG using GA

A genetic algorithm (GA) is proposed for simultaneous power quality improvement, optimal placement and sizing of fixed capacitor banks in radial distribution networks with nonlinear loads and distributed generation (DG) imposing voltage–current harmonics. In distribution systems, nonlinear loads and DGs are often considered as harmonic sources. For optimizing capacitor placement and sizing in the distribution system, objective function includes the cost of power losses, energy losses and capacitor banks. At the same time, constraints include voltage limits, number/size of installed capacitors (at each bus) and the power quality limits of standard IEEE-519. In this study, new fitness function is used to solve the constrained optimization problem with discrete variables. Simulation results for two IEEE distorted networks (18-bus and 33-bus test systems) are presented and solutions of the proposed method are compared with those of previous methods described in the literature. The main contribution of this paper is computing the (near) global solution with a lower probability of getting stuck at a local optimum and weak dependency on initial conditions, while avoiding numerical problems in large systems. Results show that proposed method could be effectively used for optimal capacitor placement and sizing in distorted distribution systems.     

Optimization of control setting and size of shunt capacitors on distribution feeders

Loads on electric utility systems have two components: active power (measured in kilowatts) and reactive power (measured in kilovars). Active power has to be generated at the power plant, whereas reactive power can be provided by either power plants or capacitors. It is a well-known fact that shunt power capacitors are the most economical source to meet the reactive power requirements of inductive loads and transmission lines operating at a lagging power factor.This paper describes new contributions to the problem of optimization of size and control setting of shunt capacitors on distribution feeders, so that the losses along the feeder are minimized. The variation of the KVAR of the load on the feeder with the distance from the substation is assumed to be linear. The parameters of this function are estimated from the available KVAR loading on the feeder first by using least-square techniques and then by using least-absolute-value parameter estimation techniques. The results obtained are compared with that obtained if the current profile is assumed to be uniformly distributed on the feeder. Our results show that the optimum size of the capacitor bank as well as its optimum location depend on the parameters of the model used for the load. Also, our results show a large saving in the size of the capacitor banks used with a considerable per-unit-loss reduction along the feeder.This work was supported by the National Science and Engineering Research Council of Canada, Grant No. A4146. The first author acknowledges the help received from Engineer Samy Soliman for reviewing all the mathematical expressions in this paper.     

A pseudo-polynomial algorithm for optimal capacitor placement on electric power distribution networks

Allocation of shunt capacitor banks on radial electric power distribution networks allow reduction of energy losses and aggregated benefits. Four decades ago Durán proposed the use of dynamic programming to find optimal capacitor placement on these networks; however, with the restricting assumption of single-ended networks, which precluded its application to real capacitor allocation problems. Subsequently heuristic methods prevailed in the capacitor allocation literature. Here the Extended Dynamic Programming Approach (EDP) lifts Durán’s restricting assumption; a richer definition of state and the projection of multidimensional informations into equivalent one-dimensional representations are the supporting concepts. In addition to allow consideration of multi-ended networks, EDP deals with other requirements of capacitor allocation studies, including the use of both fixed and switched capacitors and representation of voltage drops along the networks. When switched capacitors are considered the optimization procedure also solves the capacitor control problem, obtaining the best tap adjustments for them. Case studies with real scale distribution networks put into perspective the benefits of the methodology; EDP has the appeal of providing global optimal solutions with pseudo-polynomial computational complexity in the worst-case, and with linear complexity for practical applications.     

Restricted power domination and fault-tolerant power domination on grids

The power domination problem is to find a minimum placement of phase measurement units (PMUs) for observing the whole electric power system, which is closely related to the classical domination problem in graphs. For a graph G=(V,E), the power domination number of G is the minimum cardinality of a set S⊆V such that PMUs placed on every vertex of S results in all of V being observed. A vertex with a PMU observes itself and all its neighbors, and if an observed vertex with degree d>1 has only one unobserved neighbor, then the unobserved neighbor becomes observed. Although the power domination problem has been proved to be NP-complete even when restricted to some special classes of graphs, Dorfling and Henning in [M. Dorfling, M.A. Henning, A note on power domination in grid graphs, Discrete Applied Mathematics 154 (2006) 1023-1027] showed that it is easy to determine the power domination number of an n×m grid. Their proof provides an algorithm for giving a minimum placement of PMUs. In this paper, we consider the situation in which PMUs may only be placed within a restricted subset of V. Then, we present algorithms to solve this restricted type of power domination on grids under the conditions that consecutive rows or columns form a forbidden zone. Moreover, we also deal with the fault-tolerant measurement placement in the designed scheme and provide approximation algorithms when the number of faulty PMUs does not exceed 3.     

A new multiobjective allocator of capacitor banks and distributed generations using a new investigated differential evolution

This article has investigated a new multiobjective allocation of optimal sizing and sitting of distributed generation (DG) units and capacitor banks in simultaneous mode to improve reliability and reduce energy losses. The proposed method consists of four objectives, that is, cost of energy not supplied, system average interruption duration index, costs of energy loss and investment. A novel structure differential evolution has been suggested to solve this nonlinear complex problem and its results are compared with related values of genetic algorithm and simple differential evolutionary algorithm. In addition to the novel objective function, the other contribution of this article is proposing a new model for load and energy cost. Three types of DGs, that is, wind turbine, solar cell, and diesel generator have been used in placement process. To verify the comprehensiveness of the proposed function, three scenarios have been introduced: scenario i: first, placement of DGs, then capacitor banks, scenario ii: first, placement of capacitor banks, and then DGs, and scenario iii: simultaneous placement of DGs and capacitor banks. Simulations have been carried out on one part of practical distribution network in Metropolitan Tabriz in North West of Iran. The results of simulations have been discussed and analyzed using the five novel indices. The obtained simulation results using proposed function shows that the simultaneous placement of DGs and capacitor banks results in more reduction of the energy losses and increase improvements of reliability indices as well as voltage profile. © 2013 Wiley Periodicals, Inc. Complexity 19: 40–54, 2014     

Optimal placement and sizing of capacitor using Limaçon inspired spider monkey optimization algorithm

The power system is a complex interconnected network which can be subdivided into three components: generation, distribution, and transmission. Capacitors of specific sizes are placed in the distribution network so that losses in transmission and distribution is minimum. But the decision of size and position of capacitors in this network is a complex optimization problem. In this paper, Limaçon curve inspired local search strategy (LLS) is proposed and incorporated into spider monkey optimization (SMO) algorithm to deal optimal placement and the sizing problem of capacitors. The proposed strategy is named as Limaçon inspired SMO (LSMO) algorithm. In the proposed local search strategy, the Limaçon curve equation is modified by incorporating the persistence and social learning components of SMO algorithm. The performance of LSMO is tested over 25 benchmark functions. Further, it is applied to solve optimal capacitor placement and sizing problem in IEEE-14, 30 and 33 test bus systems with the proper allocation of 3 and 5-capacitors. The reported results are compared with a network without a capacitor (un-capacitor) and other existing methods.     

Financial planning for the preventive maintenance of power distribution systems via fuzzy AHP

One of the most important objectives of electricity distribution companies is to improve the reliability of the distribution networks. To this end, the electricity distribution companies try to optimally use the existing financial resources in the planning of preventive maintenance (PM) programs to reduce the imposed costs on the system due to the failure of network components and to improve the network reliability. In fuzzy analytical hierarchical process (fuzzy AHP) method, the degree of network reliability and the effectiveness of PM budget in the improvement of network reliability are selected as decision criteria in the budget allocation procedure. The areas served by the power distribution network are prioritized relative to each other and are assigned weights based on these priorities. The PM budget is determined based on the obtained weights. The medium voltage distribution network of seven areas in the city of Tehran have been selected for the implementation of the proposed method and the analysis of the obtained results. © 2014 Wiley Periodicals, Inc. Complexity 21: 36–46, 2016     

An analytical methodology for assessment of smart monitoring impact on future electric power distribution system reliability

Smart grid is referred to a modernized power grid which can mitigate fault detection and allow self‐healing of the system without the intervention of operators. This article proposes an innovative analytical formulation using Markov method to evaluate electric power distribution system reliability in smart grids, which incorporates the impact of smart monitoring on the overall system reliability. An accurate reliability model of the main network components and the communication infrastructure have been also considered in the methodology. The proposed approach was applied to a well‐known test bed (Roy Billinton Test System) and various reliability case studies with monitoring provision and monitoring deficiency are analyzed. This article involves the developing possibilities of communication technologies and next‐generation control systems of the entire smart network based on the real‐time monitoring and modern control system to achieve a reliable, economical, safe, and high efficiency of electricity. The implementations indicate that using an appropriate set of the smart grid monitoring devices for power system components can virtually influence all the reliability indices although the amount of improvement varies between techniques. The proposed approach determined that smart monitoring for which components of the electric power distribution systems are tailored and deduce to major economical benefits. The described approach also reveals which reliability indices drastically influenced using monitoring. © 2014 Wiley Periodicals, Inc. Complexity 21: 99–113, 2015     

Convex quadratic relaxations for mixed-integer nonlinear programs in power systems

This paper presents a set of new convex quadratic relaxations for nonlinear and mixed-integer nonlinear programs arising in power systems. The considered models are motivated by hybrid discrete/continuous applications where existing approximations do not provide optimality guarantees. The new relaxations offer computational efficiency along with minimal optimality gaps, providing an interesting alternative to state-of-the-art semidefinite programming relaxations. Three case studies in optimal power flow, optimal transmission switching and capacitor placement demonstrate the benefits of the new relaxations.     

A dynamic model of power metal-oxide-semiconductor field-effect transistor half-bridges for the fast simulation of switching induced electromagnetic emissions

Hard switching of semiconductors is the main source of conducted electromagnetic emissions (EME) in pulse-width modulation (PWM) driven power inverters. The requirements on the electromagnetic compatibility grow with the increasing number of installed electric motor drives and inductive power converters. An accurate prediction of the conducted EME requires a model which considers the switching transition of the power semiconductors and the parasitic elements. This typically leads to complex SPICE models, which are hardly suitable for fast dynamic simulations and model-based controller design. This paper presents a compact mathematical model of a low voltage half-bridge inverter, which is based on large-signal models for the individual components and allows for the fast simulation of the conducted EME and switching losses. The high accuracy of the proposed mathematical model is demonstrated by measurement results. In particular, it is shown that the model is able to accurately predict the conducted electromagnetic emissions up to 100 MHz.     

Second order fully discrete defect‐correction scheme for nonstationary conduction‐convection problem at high Reynolds number

This survey enfolds rigorous analysis of the defect‐correction finite element (FE) method for the time‐dependent conduction‐convection problem which based on the Crank‐Nicolson scheme. The method consists of two steps: solve a nonlinear problem with an added artificial viscosity term on a FE grid and correct the solutions on the same grid using a linearized defect‐correction technique. The stability and optimal error estimate of the fully discrete scheme are derived. As a consequence, the effectiveness of the method to deal with high Reynolds number is illustrated in several numerical experiments. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 681–703, 2017     

Analysis of voltages induced on power outlets due to atmospheric discharges on Radio Base Stations

For the first time, full-wave simulations regarding voltages induced on power outlets installed inside buildings, due to lightning strokes on a Radio Base Station located nearby, are performed. The scenario consists of nine buildings with outlets connected to low-voltage distribution lines, conductive ground, a Radio Base Station and grounding systems. Loads connected to the power outlets are also considered. This scenario was modeled with a computer software developed in this work that can numerically represent/model real-world complex structures with realistic parameters. In order to obtain realistic results, Maxwell’s equations are solved numerically by using the FDTD method, which generates full-wave solutions of the problems. Here, electrical conductors are represented with the aid of a thin-wire technique. The analyzed domain is truncated by using the UPML formulation. In order to deal with large tridimensional numerical models, a Beowulf cluster with 16 CPUs is used to accelerate the calculation process. The induced voltages at the energy sockets inside the buildings have been calculated initially without an electric grounding mesh connected to them. In a second moment, the calculation of these induced voltages has been performed for the same structure with a grounding mesh connected to it. In a third simulation, electric loads with resistive–inductive characteristics have been added to the scenario (connected to the energy sockets), simulating residential equipment.     

A novel of fuzzy PSS based on new objective function in multimachine power system

This article proposed a new control strategy based on Takagi–Sugeno fuzzy model for deceasing the power system oscillation. This controller is based on the parallel distributed compensation structure, the stability of the whole closed‐loop model is provided using a general Lyapunov‐Krasovski functional. Also, in this article, a new objective function has been considered to test the proposed Fuzzy Power System Stabilizer in different load conditions which increase the system damping after the system undergoes a disturbance. So, for testing the effectiveness of the proposed controller, the damping factor, damping ratio, and a combination of the damping factor and damping ratio were analyzed and compared with the proposed objective function. The effectiveness of the proposed strategy has been used over 16 machine 68 bus power system. The eigenvalue analysis and nonlinear time domain simulation results proof the effectiveness of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity 21: 288–298, 2016     

Optimization of power production through coordinated use of hydroelectric and conventional power units

In the present work a methodology to tackle the problem of simultaneous utilization of hydroelectric and conventional power units with the goal of optimizing power production operations over the short term is presented. Most problem formulations found in the literature result in the development of nonlinear optimization programs, which are solved with stochastic methods. The methodology presented in this paper leads to the development of a convex mixed integer quadratic programming (MIQP) model, which is a special type of nonlinear model that enables reaching the global optimum solution in short computational time. The efficiency of the proposed approach is demonstrated by its application to a realistic power production system.     

Mathematical Modelling of Diesel-Electric Propulsion Systems for Marine Vessels

This article presents a mathematical model of a complete diesel-electric propulsion system, including components as diesel generators, distribution network, variable speed thruster-drives, and conventional motor loads. The model is split into two parts: One power generating part where the load is specified with an aggregated active and reactive power load demand. Secondly, a power consumption part where the effects of the different load types as thruster drives, motors and other loads are modelled. The model is written in a state-space form suitable for the purpose of simulation and control design. PID-controllers represent speed governors and automatic voltage regulators.     

A Two‐Parameter Stabilized Finite Element Method for Incompressible Flows

Based on two‐grid discretizations, a two‐parameter stabilized finite element method for the steady incompressible Navier–Stokes equations at high Reynolds numbers is presented and studied. In this method, a stabilized Navier–Stokes problem is first solved on a coarse grid, and then a correction is calculated on a fine grid by solving a stabilized linear problem. The stabilization term for the nonlinear Navier–Stokes equations on the coarse grid is based on an elliptic projection, which projects higher‐order finite element interpolants of the velocity into a lower‐order finite element interpolation space. For the linear problem on the fine grid, either the same stabilization approach (with a different stabilization parameter) as that for the coarse grid problem or a completely different stabilization approach could be employed. Error bounds for the discrete solutions are estimated. Algorithmic parameter scalings of the method are also derived. The theoretical results show that, with suitable scalings of the algorithmic parameters, this method can yield an optimal convergence rate. Numerical results are provided to verify the theoretical predictions and demonstrate the effectiveness of the proposed method. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 425–444, 2017     

Interior point models for power system stability problems

In this paper, a detailed analysis of the use of optimization techniques in the study of voltage stability problems, leading to the incorporation of voltage stability criteria in traditional Optimal Power Flow (OPF) formulations is presented. Optimal power flow problems are highly nonlinear programming problems that are used to find the optimal control settings in electrical power systems. The relationship between the Lagrangian Multipliers of the OPF problem and the classification of the maximum loading point level of the system is given. Finally, the paper presents a sequential OPF technique to enhance voltage stability using reactive power and voltage rescheduling with no increase in real (active) generation cost.     

Time transformed mixed integer optimal control problems with impacts

The solutions of mixed integer optimal control problems (MIOCPs) yield optimized trajectories for dynamical systems with instantly changing dynamical behavior. The instant change is caused by a changing value of the integer valued control function. For example, a changing integer value can cause a car to change the gear, or a mechanical system to close a contact. The direct discretization of a MIOCP leads to a mixed integer nonlinear program (MINLP) and can not be solved with gradient based optimization methods at once. We extend the work by Gerdts [1] and reformulate a MIOCP with integer dependent constraints as an ordinary optimal control problem (OCP). The discretized OCP can be solved using gradient based optimization methods. We show how the integer dependent constraints can be used to model systems with impact and present optimized trajectories of computational examples, namely of a lockable double pendulum and an acyclic telescope walker. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal discrete long-term operation of nuclear-hydrothermal power systems

We discuss in this paper an algorithm for solving the optimal long-term operating problem of a hydrothermal-nuclear power system by application of the minimum norm optimization technique. The algorithm proposed here has the ability to deal with large-scale power systems and with equality and/or inequality constraints on the variables. A discrete model for the xenon and iodine concentrations is used, as well as a discrete model for hydro reservoirs. The optimization is done on a monthly time basis. For simplicity of the problem formulation, the transmission line losses are considered as a part of the load.This work supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. A4146.     

风电功率波动特性的概率分布模型研究

为保证电网安全稳定运行,在大规模风电并网运行控制过程中,准确构建风电出力波动特性的概率分布模型具有重要意义.基于数据驱动的方法,采用加权高斯混合概率分布模型来拟合大规模风电基地的波动特性,模型拟合参数可采用基于期望最大化(Expectation Maximization,EM)的极大似然估计算法来获得,并提出了拟合评价指标来与其它多种概率分布模型进行对比,结果验证了加权高斯混合概率模型的有效性和适用性.