A mixed integer programme for optimal static capacitor allocation in power systems

A method is presented for the determination of optimal size and location of static capacitor installations in a power system network for maintenance of the bus voltage magnitudes within prescribed limits under highly loaded or outage conditions. The problem is formulated as an optimization problem with the objective function representing the cost of capacitor installations and the constraints represent the reactive power flow equation of the system and the limits on the variations of the tap settings of the tap changing transformers and the generator bus voltages. The generator bus voltage magnitudes are continuously variable and the capacitor units to be installed and the tap settings are treated as discrete or integer variables. By partioning the variables into control and controlled quantities, a number of variables are eliminated from the problem. The problem is then decomposed into two smaller subproblems with integer or continuous variables. These result in the reduction of the computer memory and time requirements.     

Comprehensive learning particle swarm optimization for reactive power dispatch

Reactive power dispatch (RPD) is an optimization problem that reduces grid congestion by minimizing the active power losses for a fixed economic power dispatch. RPD reduces power system losses by adjusting the reactive power control variables such as generator voltages, transformer tap-settings and other sources of reactive power such as capacitor banks and provides better system voltage control, resulting in an improved voltage profile, system security, power transfer capability and over all system operation. In this paper, RPD problem is solved using particle swarm optimization (PSO). To overcome the drawback of premature convergence in PSO, a learning strategy is introduced in PSO, and this approach called, comprehensive learning particle swarm optimization (CLPSO) is also applied to this problem and a comparison of results is made between these two. Three different test cases have been studied such as minimization of real power losses, improvement of voltage profile and enhancement of voltage stability through a standard IEEE 30-bus and 118-bus test systems and their results have been reported. The study results show that the approaches developed are feasible and efficient.     

HAVC系统变电站多目标优化控制策略

变电站电压无功控制是电网混成自动电压控制(hybrid automatic voltage control,HAVC)系统的重要组成部分,其控制措施一般包括变电站有载调压变压器(OLTC)的调节和站内电容电抗器的投切等.变电站电压无功控制器设计是一个典型的多目标优化问题.即在调控过程中,既要控制无功及电压尽量接近设定值,又必须使OLTC的调节次数和电容电抗器的投切次数尽量少.因此,本文首先建立了HAVC系统变电站电压无功控制的多目标优化模型,然后求解该多目标优化问题得到变电站电压无功优化控制策略.对东北电网沙岭变电站的仿真分析证明了所提出的控制策略的有效性和正确性.     

A multiobjective approach for optimal placement and sizing of distributed generators and capacitors in distribution network

Both active and reactive power play important roles in power system transmission and distribution networks. While active power does the useful work, reactive power supports the voltage that necessitates control from system reliability aspect as deviation of voltage from nominal range may lead to inadvertent operation and premature failure of system components. Reactive power flow must also be controlled in the system to maximize the amount of real power that can be transferred across the power transmitting media. This paper proposes an approach to simultaneously minimize the real power loss and the net reactive power flow in the system when reinforced with distributed generators (DGs) and shunt capacitors (SCs). With the suggested method, the system performance, reliability and loading capacity can be increased by reduction of losses. A multiobjective evolutionary algorithm based on decomposition (MOEA/D) is adopted to select optimal sizes and locations of DGs and SCs in large scale distribution networks with objectives being minimizing system real and reactive power losses. MOEA/D is the process of decomposition of a multiobjective optimization problem into a number of scalar optimization subproblems and optimizing those concurrently. Case studies with standard IEEE 33-bus, 69-bus, 119-bus distribution networks and a practical 83-bus distribution network are performed. Output results of MOEA/D method are compared with similar past studies and notable improvement is observed.     

A hybrid method of chaotic particle swarm optimization and linear interior for reactive power optimisation

The reactive power optimization is an effective method to improve voltage level, decrease network losses and maintain the power system running under normal conditions. This paper provides a method combining particle swarm optimization (PSO) with linear interior point to handle the problems remaining in the traditional arithmetic of time-consuming convergence and demanding initial values. Furthermore, since chaotic mapping enjoys certainty, ergodicity and stochastic property, the paper introduces chaos mapping into the particle swarm optimization, the paper presents a new arithmetic based on a hybrid method of chaotic particle swarm optimization and linear interior point. Thanks to the superior overall exploration ability of particle swarm optimization and the local exploration ability of linear interior point within the neighborhood of the optimal point, the new method can improve the performance of both convergence and results’ precision. Tested by IEEE-30, the new method provided in this paper is proved effective and practical in the optimization of shunt capacitors and tap position of load-ratio voltage transformer.     

A new method for optimal location and sizing of capacitors in distorted distribution networks using PSO algorithm

This paper presents an optimization algorithm for simultaneous improvement of power quality (PQ), optimal placement and sizing of fixed capacitor banks in radial distribution networks in the presence of voltage and current harmonics. The algorithm is based on particle swarm optimization (PSO). The objective function includes the cost of power losses, energy losses and those of the capacitor banks. Constraints include voltage limits, number/size of installed capacitors at each bus, and PQ limits of standard IEEE-519. Using a newly proposed fitness function, a suitable combination of the objective function and relevant constraints is defined as a criterion to select a set of the most suitable buses for capacitor placement. This method is also capable of improving particles in several steps for both converging more readily to the near global solution as well as improving satisfaction of the power quality constraints. Simulation results for the 18-bus and 33-bus IEEE distorted networks using the proposed method are presented and compared with those of previous works. In the 18-bus IEEE distorted network, this indicated an improvement of 3.29% saving compared with other methods. Using the proposed optimization method and simulation performed on the 33-bus IEEE distorted network an annual cost reduction of 31.16% was obtained.     

高压电容取电技术的研究与设计

针对传统技术中采用电压互感器分压带来的不便,设计出基于电容式高压取电的新型取电设备。该设备将电容、变压器串联构成串联电路,由此实施高压取电;利用电容式高压取电原理,设计了新型的高压取电电容;在电路中增加继电器监测单元和过电流监测单元,保证了电路的安全性;通过电容分压,有效地将电路中的高压转换为低压,将得到的电能存储到超级电容器组中,超级电容器组用作供能装置向电力线电网线路中的负载输出电能,供负载使用。试验表明,采用电容式分压原理进行高压取电,不仅用法灵活,减轻了电力线路的运行负担,还提高了带载能力,具有较好的实用价值。     

Optimal reactive power dispatch for real power loss minimization and voltage stability enhancement using Artificial Bee Colony Algorithm

Reactive Power Dispatch (RPD) plays important role in power system reliability and security. This paper proposes the Optimal Reactive Power Dispatch (ORPD) for real power loss minimization, voltage deviation minimization and voltage stability enhancement using Artificial Bee Colony (ABC) Algorithm. ORPD is a mixed integer nonlinear optimization problem which includes both continuous and discrete control variables. The ABC algorithm is used to find the setting of control variables such as generator voltage magnitude, tap position of tap changing transformer and reactive power output of the compensation devices. The proposed algorithm is tested on IEEE 30 and 57 bus systems, Simulation results show that the proposed approach converges to better solutions and much faster than the earlier reported approaches in the literature. The optimization strategy is general and can be used to solve other power system optimization problems.     

Differential evolution approach for optimal reactive power dispatch

Differential evolution based optimal reactive power dispatch for real power loss minimization in power system is presented in this paper. The proposed methodology determines control variable settings such as generator terminal voltages, tap positions and the number of shunts to be switched, for real power loss minimization in the transmission system. The problem is formulated as a mixed integer nonlinear optimization problem. A generic penalty function method, which does not require any penalty coefficient, is employed for constraint handling. The formulation also checks for the feasibility of the optimal control variable setting from a voltage security point of view by using a voltage collapse proximity indicator. The algorithm is tested on standard IEEE 14, IEEE 30, and IEEE 118-Bus test systems. To show the effectiveness of proposed method the results are compared with Particle Swarm Optimization and a conventional optimization technique – Sequential Quadratic Programming.     

Modeling a mixed-integer-binary small-population evolutionary particle swarm algorithm for solving the optimal power flow problem in electric power systems

This research discusses the application of a mixed-integer-binary small-population-based evolutionary particle swarm optimization to the problem of optimal power flow, where the optimization problem has been formulated taking into account four decision variables simultaneously: active power (continuous), voltage generator (continuous), tap position on transformers (integer) and shunt devices (binary). The constraint handling technique used in the algorithm is based on a strategy to generate and keep the decision variables in feasible space through the heuristic operators. The heuristic operators are applied in the active power stage and the reactive power stage sequentially. Firstly, the heuristic operator for the power balance is computed in order to maintain the power balance constraint through a re-dispatch of the thermal units. Secondly, the heuristic operators for the limit of active power flows and the bus voltage constraint at each generator bus are executed through the sensitivity factors. The advantage of our approach is that the algorithm focuses the search of the decision variables on the feasible solution space, obtaining a better cost in the objective function. Such operators not only improve the quality of the final solutions but also significantly improve the convergence of the search process. The methodology is verified in several electric power systems.     

电容器的火灾预防及群爆处理方法

电力电容器,具有改善电力系统的电压质量和提高输电线路的输电能力,是电力系统的重要设备。电容器在运行过程中,可能发生火灾,并联电容器单台保护熔断器会出现群爆现象,从而导致电容器无法正常工作。分析了电容器火灾产生原因及预防措施,电容器群爆的处理等。     

Using the gray wolf optimizer for solving optimal reactive power dispatch problem

This paper presents the use of a new meta-heuristic technique namely gray wolf optimizer (GWO) which is inspired from gray wolves’ leadership and hunting behaviors to solve optimal reactive power dispatch (ORPD) problem. ORPD problem is a well-known nonlinear optimization problem in power system. GWO is utilized to find the best combination of control variables such as generator voltages, tap changing transformers’ ratios as well as the amount of reactive compensation devices so that the loss and voltage deviation minimizations can be achieved. In this paper, two case studies of IEEE 30-bus system and IEEE 118-bus system are used to show the effectiveness of GWO technique compared to other techniques available in literature. The results of this research show that GWO is able to achieve less power loss and voltage deviation than those determined by other techniques.     

Momentum-based wavelet and double wavelet neural networks for power system applications

In order to minimize the power loss and to control the voltage in the power systems, the proposed momentum-based wavelet neural network and proposed momentum-based double wavelet neural network are proposed in this paper. The training data are obtained by using linear programming method by solving several abnormal conditions. The control variables considered are generator voltages and transformer taps, and the dependent variables are generator reactive powers and load bus voltages. The IEEE 14-bus system and IEEE 30-bus system are tested using the linear programming, Levenberg–Marquardt artificial neural network, proposed momentum-based wavelet neural network and proposed momentum-based double wavelet neural network to validate the effectiveness of the proposed MDWNN method. The trained neural networks are capable of controlling the voltage, and reactive power in power systems is proved by the results with the high level of precision and speed.

     

Weighted elitism based Ant Lion Optimizer to solve optimum VAr planning problem

In this paper, a newly proposed Ant-Lion Optimizer (ALO) is applied to solve Optimal Reactive Power Dispatch (ORPD) problem of power system. The ORPD is a VAr planning problem and is a highly non linear, non convex, challenging optimization problem; usually devised as constrained Optimal Power Flow (OPF). This paper also proposes the improvement in the search capability of ALO. A novel weighted elitism concept is introduced in the elitism phase of the original ALO to improve the exploration property of the algorithm. The proposed Modified ALO (MALO) intelligently balances both exploration and exploitation, which enhances the hunting capability of ALO. Both ALO and MALO is used to determine the optimal settings of generator voltages, tap positions of tap changer transformers and VAr output of shunt capacitors to optimize objectives: like, the active power loss, total voltage deviation and voltage stability index. The proposed algorithm is programmed and simulated on MATLB and tested on IEEE-30 and 57 bus systems. The results are compared with ALO and other methods. The effectiveness of MALO is further verified by solving few benchmark mathematical functions. The numerical results reveal that, MALO gives better optimum solutions for the benchmark functions compare to original ALO and outperforms several other methods used in the literature to solve ORPD problems. The t-Test and parametric analysis confirms the robustness and consistency of the MALO over ALO and other similar methods.     

基于能量流动双PWM协调控制

基于双PWM结构,根据系统能量流动分析系统在能量平衡状态和能量不平衡状态下系统各部分间的能量关系,并建立双PWM结构能量数学模型;针对系统输出能量与消耗能量不平衡时造成的直流母线电压波动以及输出功率不匹配的问题,建立关于直流母线电压以及网侧电流d轴分量的约束条件,保证系统能量能够平滑变化;采用约束条件对整流器电压外环以及功率内环进行修正,用以实现整流侧输出能量与逆变侧消耗能量的快速平衡,达到双PWM结构间协调控制的目的;根据仿真结果表明,系统在电机功率突变时,能够实现能量的快速平衡,并且能够减少直流母线电压波动,减少网侧谐波分量和直流侧电容。     

Analyzing the multi objective analytical aspects of distribution systems with multiple multi-type compensators using modified cuckoo search algorithm

This paper presents a two stage solution strategy to solve multi objective optimization problem in the presence of capacitors, distributed generators (DGs) and automatic voltage regulators (AVRs) for better planning and operation of a primary distribution system. Using this, the economical aspects such as net savings and the technical aspects such as voltage deviation and section current index objectives are optimized while satisfying system equality and in-equality constraints. The optimum number of compensating devices and their optimal locations are identified in a given system so as to enhance the system security by minimizing the system power losses. The proposed methodology of finding the optimal sizes of compensating devices with multi-objective functions uses fuzzy decision approach to select the best compromised solution from the total generation Pareto solution as per the operators’ requirement. The feasibility and effectiveness of the proposed method are examined on standard 15-node, 33-node and 69-node test systems. According to the analytical results, the proposed framework in the presence of compensating devices enhances the system performance more effectively.     

Minimization of voltage deviation and power losses in power networks using Pareto optimization methods

Voltage regulation is an important task in electrical engineering for controlling node voltages in a power network. A widely used solution for the problem of voltage regulation is based on adjusting the taps in under load tap changers (ULTCs) power transformers and, in some cases, turning on Flexible Alternating Current Transmission Systems (FACTS), synchronous machines or capacitor banks in the substations. Most papers found in the literature dealing with this problem aim to avoid voltage drops in radial networks, but few of them consider power losses or meshed networks. The aim of this paper is to present and evaluate the performance of several multi-objective algorithms, including hybrid approaches, in order to minimize both voltage deviation and power losses by operating ULTCs located in high voltage substations. In particular, a well-known multi-objective algorithm, PAES, is used for this purpose. PAES finds a set of solutions according to Pareto-optimization concepts. Furthermore, this algorithm is hybridized with simulated annealing and tabu search to improve the quality of the solutions. The implemented algorithms are evaluated using two test networks, and the numerical results are analyzed with two metrics often used in the multi-objective field. The results obtained demonstrate the good performance of these algorithms.     

Pareto‐Set Based Multi‐Objective Dynamic Reactive Power and Voltage Control

A novel approach is proposed in this paper to solve multi‐objective dynamic reactive power and voltage control (Volt/VAR control, VVC). The method is able to attain the Pareto‐optimal solutions, based on the day‐ahead load forecast, for the VVC considering reducing daily power loss, enhancing voltage profile and optimizing dispatch schedules for on‐load tap changer (OLTC) and shunt capacitor switching, which will provide decision maker more options to schedule the dynamic VVC. This approach is simulated in IEEE14 buses system and IEEE30 buses system, and the results are encouraging with respect to performance in dynamic reactive power control. Moreover, the application in an actual distribution system verifies its effectiveness further.     

Chaotic krill herd algorithm for optimal reactive power dispatch considering FACTS devices

Conventionally, optimal reactive power dispatch (ORPD) is described as the minimization of active power transmission losses and/or total voltage deviation by controlling a number of control variables while satisfying certain equality and inequality constraints. This article presents a newly developed meta-heuristic approach, chaotic krill herd algorithm (CKHA), for the solution of the ORPD problem of power system incorporating flexible AC transmission systems (FACTS) devices. The proposed CKHA is implemented and its performance is tested, successfully, on standard IEEE 30-bus test power system. The considered power system models are equipped with two types of FACTS controllers (namely, thyristor controlled series capacitor and thyristor controlled phase shifter). Simulation results indicate that the proposed approach yields superior solution over other popular methods surfaced in the recent state-of-the-art literature including chaos embedded few newly developed optimization techniques. The obtained results indicate the effectiveness for the solution of ORPD problem of power system considering FACTS devices. Finally, simulation is extended to some large-scale power system models like IEEE 57-bus and IEEE 118-bus test power systems for the same objectives to emphasis on the scalability of the proposed CKHA technique. The scalability, the robustness and the superiority of the proposed CKHA are established in this paper.     

A magnetoelectric energy harvester and management circuit for wireless sensor network

This paper presents an electromagnetic energy harvesting scheme by using a composite magnetoelectric (ME) transducer and a power management circuit. In the transducer, the vibrating wave induced from the magnetostrictive Terfenol-D plate in dynamic magnetic field is converged by using an ultrasonic horn. Consequently more vibrating energy can be converted into electricity by the piezoelectric element. A switching capacitor network for storing electricity is developed. The output of the transducer charges the storage capacitors in parallel until the voltage across the capacitors arrives at the threshold, and then the capacitors are automatically switched to being in series. More capacitors can be employed in the capacitor network to further raise the output voltage in discharging. For the weak magnetic field environment, an active magnetic generator and a magnetic coil antenna under ground are used for producing an ac magnetic field of 0.2–1 Oe at a distance of 25–50 m. In combination with the supply management circuit, the electromagnetic energy harvester with a rather weak power output (about 20 μW) under an ac magnetic field of 1 Oe can supply power for wireless sensor nodes with power consumption of 75 mW at a duration of 620 ms.